Pub Date : 2025-01-02DOI: 10.1103/physrevx.15.011001
Wen-Tao Xu, Tibor Rakovszky, Michael Knap, Frank Pollmann
We explore the relationship between higher-form symmetries and entanglement properties in lattice gauge theories with discrete gauge groups, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on a generalization of the Fradkin-Shenker model describing Z2 lattice gauge theory with matter, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered deconfined phase and a nontrivial SPT phase protected by a 1-form and a 0-form symmetry, among others. We obtain the following key findings: First, the entanglement properties of the model depend on whether the 1-form symmetries and the Gauss law constraint are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the nontrivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy turns out to be fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the nontrivial SPT phase, we find that spontaneous higher-form symmetry breaking removes “half” of the ES levels, leading to a nondegenerate ES in the topologically ordered phase, in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but it is fragile when the 1-form symmetry is exact. Our results demonstrate the advantage of higher-form symmetries for understanding entanglement properties of gauge theories. Published by the American Physical Society2025
{"title":"Entanglement Properties of Gauge Theories from Higher-Form Symmetries","authors":"Wen-Tao Xu, Tibor Rakovszky, Michael Knap, Frank Pollmann","doi":"10.1103/physrevx.15.011001","DOIUrl":"https://doi.org/10.1103/physrevx.15.011001","url":null,"abstract":"We explore the relationship between higher-form symmetries and entanglement properties in lattice gauge theories with discrete gauge groups, which can exhibit both topologically ordered phases and higher-form symmetry-protected topological (SPT) phases. Our study centers on a generalization of the Fradkin-Shenker model describing Z</a:mi>2</a:mn></a:msub></a:math> lattice gauge theory with matter, where the Gauss law constraint can be either emergent or exact. The phase diagram includes a topologically ordered deconfined phase and a nontrivial SPT phase protected by a 1-form and a 0-form symmetry, among others. We obtain the following key findings: First, the entanglement properties of the model depend on whether the 1-form symmetries and the Gauss law constraint are exact or emergent. For the emergent Gauss law, the entanglement spectrum (ES) of the nontrivial SPT phase exhibits degeneracies, which are robust at low energies against weak perturbations that explicitly break the exact 1-form symmetry. When the Gauss law and the 1-form symmetry are both exact, the ES degeneracy is extensive. This extensive degeneracy turns out to be fragile and can be removed completely by infinitesimal perturbations that explicitly break the exact 1-form symmetry while keeping the Gauss law exact. Second, we consider the ES in the topologically ordered phase where 1-form symmetries are spontaneously broken. In contrast to the ES of the nontrivial SPT phase, we find that spontaneous higher-form symmetry breaking removes “half” of the ES levels, leading to a nondegenerate ES in the topologically ordered phase, in general. Third, we derive a connection between spontaneous higher-form symmetry breaking and the topological entanglement entropy (TEE). Using this relation, we investigate the entanglement entropy that can be distilled in the deconfined phase of the original Fradkin-Shenker model using gauge-invariant measurements. We show that the TEE is robust against the measurement when the 1-form symmetry is emergent but it is fragile when the 1-form symmetry is exact. Our results demonstrate the advantage of higher-form symmetries for understanding entanglement properties of gauge theories. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"14 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142917011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-31DOI: 10.1103/physrevx.14.041072
Zheng Li, Chao Mu, Pengfei Li, Wei Wu, Jiangping Hu, Tao Xiang, Kun Jiang, Jianlin Luo
The Hebel-Slichter coherence peak, observed in the spin-lattice relaxation rate 1</a:mn>/</a:mo>T</a:mi>1</a:mn></a:msub></a:math> just below the critical temperature <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mi mathvariant="normal">c</c:mi></c:msub></c:math>, serves as a crucial experimental validation of the Bardeen-Cooper-Schrieffer pairing symmetry in conventional superconductors. However, no coherence peak in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mn>1</f:mn><f:mo>/</f:mo><f:msub><f:mi>T</f:mi><f:mn>1</f:mn></f:msub></f:math> has been observed in unconventional superconductors like cuprates. In this study, an unconventional coherence peak is identified for the first time using nuclear quadrupole resonance on <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msub><h:mrow><h:mi>YBa</h:mi></h:mrow><h:mrow><h:mn>2</h:mn></h:mrow></h:msub><h:msub><h:mrow><h:mi>Cu</h:mi></h:mrow><h:mrow><h:mn>4</h:mn></h:mrow></h:msub><h:msub><h:mrow><h:mi mathvariant="normal">O</h:mi></h:mrow><h:mrow><h:mn>8</h:mn></h:mrow></h:msub></h:mrow></h:math>, pointing to a distinctive pairing symmetry. The spin-lattice relaxation rate in nuclear quadrupole resonance and nuclear magnetic resonance with nuclear spin <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>I</k:mi><k:mo>></k:mo><k:mn>1</k:mn><k:mo>/</k:mo><k:mn>2</k:mn></k:math> comprises the magnetic relaxation rate <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>1</m:mn><m:mo>/</m:mo><m:msubsup><m:mi>T</m:mi><m:mn>1</m:mn><m:mi>mag</m:mi></m:msubsup></m:math>, which probes magnetic fluctuations, and the quadrupole relaxation rate <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>1</o:mn><o:mo>/</o:mo><o:msubsup><o:mi>T</o:mi><o:mn>1</o:mn><o:mrow><o:mi>quad</o:mi></o:mrow></o:msubsup></o:math>, which probes charge fluctuations. By utilizing <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mmultiscripts><q:mrow><q:mi>Cu</q:mi></q:mrow><q:mprescripts/><q:none/><q:mrow><q:mn>63</q:mn></q:mrow></q:mmultiscripts></q:mrow></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mmultiscripts><s:mrow><s:mi>Cu</s:mi></s:mrow><s:mprescripts/><s:none/><s:mrow><s:mn>65</s:mn></s:mrow></s:mmultiscripts></s:mrow></s:math> isotopes, we successfully distinguish <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mn>1</u:mn><u:mo>/</u:mo><u:msubsup><u:mi>T</u:mi><u:mn>1</u:mn><u:mi>mag</u:mi></u:msubsup></u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1</w:mn><w:mo>/</w:mo><w:msubsup><w:mi>T</w:mi><w:mn>1</w:mn><w:mrow><w:mi>quad</w:mi></w:mrow></w:msubsup></w:math> of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mrow><y:msub><y:mrow><y:mi>YBa</y:mi></y:mrow><y:mrow><y:mn>2
{"title":"Unconventional Coherence Peak in Cuprate Superconductors","authors":"Zheng Li, Chao Mu, Pengfei Li, Wei Wu, Jiangping Hu, Tao Xiang, Kun Jiang, Jianlin Luo","doi":"10.1103/physrevx.14.041072","DOIUrl":"https://doi.org/10.1103/physrevx.14.041072","url":null,"abstract":"The Hebel-Slichter coherence peak, observed in the spin-lattice relaxation rate 1</a:mn>/</a:mo>T</a:mi>1</a:mn></a:msub></a:math> just below the critical temperature <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:msub><c:mi>T</c:mi><c:mi mathvariant=\"normal\">c</c:mi></c:msub></c:math>, serves as a crucial experimental validation of the Bardeen-Cooper-Schrieffer pairing symmetry in conventional superconductors. However, no coherence peak in <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><f:mn>1</f:mn><f:mo>/</f:mo><f:msub><f:mi>T</f:mi><f:mn>1</f:mn></f:msub></f:math> has been observed in unconventional superconductors like cuprates. In this study, an unconventional coherence peak is identified for the first time using nuclear quadrupole resonance on <h:math xmlns:h=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><h:mrow><h:msub><h:mrow><h:mi>YBa</h:mi></h:mrow><h:mrow><h:mn>2</h:mn></h:mrow></h:msub><h:msub><h:mrow><h:mi>Cu</h:mi></h:mrow><h:mrow><h:mn>4</h:mn></h:mrow></h:msub><h:msub><h:mrow><h:mi mathvariant=\"normal\">O</h:mi></h:mrow><h:mrow><h:mn>8</h:mn></h:mrow></h:msub></h:mrow></h:math>, pointing to a distinctive pairing symmetry. The spin-lattice relaxation rate in nuclear quadrupole resonance and nuclear magnetic resonance with nuclear spin <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mi>I</k:mi><k:mo>></k:mo><k:mn>1</k:mn><k:mo>/</k:mo><k:mn>2</k:mn></k:math> comprises the magnetic relaxation rate <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><m:mn>1</m:mn><m:mo>/</m:mo><m:msubsup><m:mi>T</m:mi><m:mn>1</m:mn><m:mi>mag</m:mi></m:msubsup></m:math>, which probes magnetic fluctuations, and the quadrupole relaxation rate <o:math xmlns:o=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><o:mn>1</o:mn><o:mo>/</o:mo><o:msubsup><o:mi>T</o:mi><o:mn>1</o:mn><o:mrow><o:mi>quad</o:mi></o:mrow></o:msubsup></o:math>, which probes charge fluctuations. By utilizing <q:math xmlns:q=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><q:mrow><q:mmultiscripts><q:mrow><q:mi>Cu</q:mi></q:mrow><q:mprescripts/><q:none/><q:mrow><q:mn>63</q:mn></q:mrow></q:mmultiscripts></q:mrow></q:math> and <s:math xmlns:s=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><s:mrow><s:mmultiscripts><s:mrow><s:mi>Cu</s:mi></s:mrow><s:mprescripts/><s:none/><s:mrow><s:mn>65</s:mn></s:mrow></s:mmultiscripts></s:mrow></s:math> isotopes, we successfully distinguish <u:math xmlns:u=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><u:mn>1</u:mn><u:mo>/</u:mo><u:msubsup><u:mi>T</u:mi><u:mn>1</u:mn><u:mi>mag</u:mi></u:msubsup></u:math> and <w:math xmlns:w=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><w:mn>1</w:mn><w:mo>/</w:mo><w:msubsup><w:mi>T</w:mi><w:mn>1</w:mn><w:mrow><w:mi>quad</w:mi></w:mrow></w:msubsup></w:math> of <y:math xmlns:y=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><y:mrow><y:msub><y:mrow><y:mi>YBa</y:mi></y:mrow><y:mrow><y:mn>2","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"26 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142908262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder SU(2)→U(1)→Z2→E. Our results have direct applications in experiments with quantum simulators. Published by the American Physical Society2024
{"title":"Engineering Hierarchical Symmetries","authors":"Zhanpeng Fu, Roderich Moessner, Hongzheng Zhao, Marin Bukov","doi":"10.1103/physrevx.14.041070","DOIUrl":"https://doi.org/10.1103/physrevx.14.041070","url":null,"abstract":"The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific desired properties with a high degree of control and flexibility. Here, we present such a program for the tunable generation of sequences of symmetries on controllable timescales. Concretely, our general driving protocol for many-body systems generates a sequence of prethermal regimes, each exhibiting a lower symmetry than the preceding one. We provide an explicit construction of effective Hamiltonians exhibiting these symmetries, which imprints emergent quasiconservation laws hierarchically, enabling us to engineer the respective symmetries and concomitant orders in nonequilibrium matter. We provide explicit examples, including spatiotemporal and topological phenomena, as well as a spin chain realizing the symmetry ladder SU</a:mi>(</a:mo>2</a:mn>)</a:mo></a:mrow>→</a:mo>U</a:mi>(</a:mo>1</a:mn>)</a:mo></a:mrow>→</a:mo>Z</a:mi>2</a:mn></a:msub>→</a:mo>E</a:mi></a:math>. Our results have direct applications in experiments with quantum simulators. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"64 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-27DOI: 10.1103/physrevx.14.041071
Alrik Durand, Yoann Baron, Péter Udvarhelyi, Félix Cache, Krithika V. R., Tobias Herzig, Mario Khoury, Sébastien Pezzagna, Jan Meijer, Jean-Michel Hartmann, Shay Reboh, Marco Abbarchi, Isabelle Robert-Philip, Adam Gali, Jean-Michel Gérard, Vincent Jacques, Guillaume Cassabois, Anaïs Dréau
Among the wealth of single fluorescent defects recently detected in silicon, the G center catches interest for its telecom single-photon emission that could be coupled to a metastable electron spin triplet. The G center is a unique defect where the standard Born-Oppenheimer approximation used in solid-state physics breaks down as one of its atoms, a silicon atom in interstitial position Si(i), can move between six sites. The impact of its displacement, due either to coherent tunneling or to random jumps from one site to another, on the optical properties of G centers is still largely unknown, especially in silicon-on-insulator (SOI) samples. Here, we investigate the displacement of the center of mass of the G center in silicon. By performing photoluminescence experiments at single-defect scale, we show that individual G defects in SOI exhibit several emission dipoles and zero-phonon line fine structures with splittings up to approximately 1 meV, both indicating a motion of the defect central atom over time. Combining polarization and spectral analysis at the single-photon level, we evidence that the reconfiguration dynamics is drastically different from the one of the unperturbed G center in bulk silicon where the mobile atom is fully delocalized over all six sites through tunneling. The SOI structure freezes the Si(i) delocalization of the G defect and, as a result, enables one to isolate linearly polarized optical lines. Under above-band-gap optical excitation, the central atom of G centers in SOI behaves as if it were in a six-slot roulette wheel, randomly alternating between localized crystal sites at each optical cycle. Comparative measurements in a bulk silicon sample and calculations highlight that strain is likely the dominant perturbation impacting the G center geometry. These results shed light on the importance of the atomic reconfiguration dynamics to understand and control the photoluminescence properties of the G center in silicon. More generally, these findings emphasize the impact of strain fluctuations inherent to SOI wafers for future quantum integrated photonics applications based on color centers in silicon. Published by the American Physical Society2024
{"title":"Hopping of the Center-of-Mass of Single G Centers in Silicon-on-Insulator","authors":"Alrik Durand, Yoann Baron, Péter Udvarhelyi, Félix Cache, Krithika V. R., Tobias Herzig, Mario Khoury, Sébastien Pezzagna, Jan Meijer, Jean-Michel Hartmann, Shay Reboh, Marco Abbarchi, Isabelle Robert-Philip, Adam Gali, Jean-Michel Gérard, Vincent Jacques, Guillaume Cassabois, Anaïs Dréau","doi":"10.1103/physrevx.14.041071","DOIUrl":"https://doi.org/10.1103/physrevx.14.041071","url":null,"abstract":"Among the wealth of single fluorescent defects recently detected in silicon, the G center catches interest for its telecom single-photon emission that could be coupled to a metastable electron spin triplet. The G center is a unique defect where the standard Born-Oppenheimer approximation used in solid-state physics breaks down as one of its atoms, a silicon atom in interstitial position Si</a:mi></a:mrow>(</a:mo>i</a:mi>)</a:mo></a:mrow></a:msub></a:mrow></a:math>, can move between six sites. The impact of its displacement, due either to coherent tunneling or to random jumps from one site to another, on the optical properties of G centers is still largely unknown, especially in silicon-on-insulator (SOI) samples. Here, we investigate the displacement of the center of mass of the G center in silicon. By performing photoluminescence experiments at single-defect scale, we show that individual G defects in SOI exhibit several emission dipoles and zero-phonon line fine structures with splittings up to approximately 1 meV, both indicating a motion of the defect central atom over time. Combining polarization and spectral analysis at the single-photon level, we evidence that the reconfiguration dynamics is drastically different from the one of the unperturbed G center in bulk silicon where the mobile atom is fully delocalized over all six sites through tunneling. The SOI structure freezes the <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><f:mrow><f:msub><f:mrow><f:mi>Si</f:mi></f:mrow><f:mrow><f:mo stretchy=\"false\">(</f:mo><f:mi mathvariant=\"normal\">i</f:mi><f:mo stretchy=\"false\">)</f:mo></f:mrow></f:msub></f:mrow></f:math> delocalization of the G defect and, as a result, enables one to isolate linearly polarized optical lines. Under above-band-gap optical excitation, the central atom of G centers in SOI behaves as if it were in a six-slot roulette wheel, randomly alternating between localized crystal sites at each optical cycle. Comparative measurements in a bulk silicon sample and calculations highlight that strain is likely the dominant perturbation impacting the G center geometry. These results shed light on the importance of the atomic reconfiguration dynamics to understand and control the photoluminescence properties of the G center in silicon. More generally, these findings emphasize the impact of strain fluctuations inherent to SOI wafers for future quantum integrated photonics applications based on color centers in silicon. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"202 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-26DOI: 10.1103/physrevx.14.041069
Sanjay Moudgalya, Olexei I. Motrunich
We study quantum many-body scars (QMBS) in the language of commutant algebras, which are defined as symmetry algebras of of local Hamiltonians. This framework explains the origin of dynamically disconnected subspaces seen in models with exact QMBS, i.e., the large “thermal” subspace and the small “nonthermal” subspace, which are attributed to the existence of unconventional nonlocal conserved quantities in the commutant; hence, it unifies the study of conventional symmetries and weak ergodicity-breaking phenomena into a single framework. Furthermore, this language enables us to use the von Neumann double commutant theorem to formally write down the exhaustive algebra of Hamiltonians with a desired set of QMBS, which demonstrates that QMBS survive under large classes of local perturbations. We illustrate this using several standard examples of QMBS, including the spin-1/2 ferromagnetic, AKLT, spin-1 XY π-bimagnon, and the electronic η-pairing towers of states; in each of these cases, we explicitly write down a set of generators for the full algebra of Hamiltonians with these QMBS. Understanding this hidden structure in QMBS Hamiltonians also allows us to recover results of previous “brute-force” numerical searches for such Hamiltonians. In addition, this language clearly demonstrates the equivalence of several unified formalisms for QMBS proposed in the literature and also illustrates the connection between two apparently distinct classes of QMBS Hamiltonians—those that are captured by the so-called Shiraishi-Mori construction and those that lie beyond. Finally, we show that this framework motivates a precise definition for QMBS that automatically implies that they violate the conventional eigenstate thermalization hypothesis, and we discuss its implications to dynamics. Published by the American Physical Society2024
{"title":"Exhaustive Characterization of Quantum Many-Body Scars Using Commutant Algebras","authors":"Sanjay Moudgalya, Olexei I. Motrunich","doi":"10.1103/physrevx.14.041069","DOIUrl":"https://doi.org/10.1103/physrevx.14.041069","url":null,"abstract":"We study quantum many-body scars (QMBS) in the language of commutant algebras, which are defined as symmetry algebras of of local Hamiltonians. This framework explains the origin of dynamically disconnected subspaces seen in models with exact QMBS, i.e., the large “thermal” subspace and the small “nonthermal” subspace, which are attributed to the existence of unconventional nonlocal conserved quantities in the commutant; hence, it unifies the study of conventional symmetries and weak ergodicity-breaking phenomena into a single framework. Furthermore, this language enables us to use the von Neumann double commutant theorem to formally write down the exhaustive algebra of Hamiltonians with a desired set of QMBS, which demonstrates that QMBS survive under large classes of local perturbations. We illustrate this using several standard examples of QMBS, including the spin-1</a:mn>/</a:mo>2</a:mn></a:mrow></a:math> ferromagnetic, AKLT, spin-1 XY <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>π</c:mi></c:math>-bimagnon, and the electronic <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mi>η</e:mi></e:math>-pairing towers of states; in each of these cases, we explicitly write down a set of generators for the full algebra of Hamiltonians with these QMBS. Understanding this hidden structure in QMBS Hamiltonians also allows us to recover results of previous “brute-force” numerical searches for such Hamiltonians. In addition, this language clearly demonstrates the equivalence of several unified formalisms for QMBS proposed in the literature and also illustrates the connection between two apparently distinct classes of QMBS Hamiltonians—those that are captured by the so-called Shiraishi-Mori construction and those that lie beyond. Finally, we show that this framework motivates a precise definition for QMBS that automatically implies that they violate the conventional eigenstate thermalization hypothesis, and we discuss its implications to dynamics. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"47 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-24DOI: 10.1103/physrevx.14.041068
Michał Oszmaniec, Marcin Kotowski, Michał Horodecki, Nicholas Hunter-Jones
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. Published by the American Physical Society2024
{"title":"Saturation and Recurrence of Quantum Complexity in Random Local Quantum Dynamics","authors":"Michał Oszmaniec, Marcin Kotowski, Michał Horodecki, Nicholas Hunter-Jones","doi":"10.1103/physrevx.14.041068","DOIUrl":"https://doi.org/10.1103/physrevx.14.041068","url":null,"abstract":"Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"98 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142879744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-18DOI: 10.1103/physrevx.14.041066
Tom Day, Maya Isarov, William J. Pappas, Brett C. Johnson, Hiroshi Abe, Takeshi Ohshima, Dane R. McCamey, Arne Laucht, Jarryd J. Pla
Masers once represented the state of the art in low-noise microwave amplification technology but eventually became obsolete due to their need for cryogenic cooling. Masers based on solid-state spin systems perform most effectively as amplifiers, since they provide a large density of spins and can, therefore, operate at relatively high powers. While solid-state maser oscillators have been demonstrated at room temperature, continuous-wave amplification in these systems has only ever been realized at cryogenic temperatures. Here, we report on a continuous-wave solid-state maser amplifier operating at room temperature. We achieve this feat using a practical setup that includes an ensemble of nitrogen-vacancy center spins in a diamond crystal, a strong permanent magnet, and a simple laser diode. We describe important amplifier characteristics including gain, bandwidth, compression power, and noise temperature and discuss the prospects of realizing a room-temperature near-quantum-noise-limited amplifier with this system. Finally, we show that in a different mode of operation the spins can be used to reduce the microwave noise in an external circuit to cryogenic levels, all without the requirement for physical cooling. Published by the American Physical Society2024
{"title":"Room-Temperature Solid-State Maser Amplifier","authors":"Tom Day, Maya Isarov, William J. Pappas, Brett C. Johnson, Hiroshi Abe, Takeshi Ohshima, Dane R. McCamey, Arne Laucht, Jarryd J. Pla","doi":"10.1103/physrevx.14.041066","DOIUrl":"https://doi.org/10.1103/physrevx.14.041066","url":null,"abstract":"Masers once represented the state of the art in low-noise microwave amplification technology but eventually became obsolete due to their need for cryogenic cooling. Masers based on solid-state spin systems perform most effectively as amplifiers, since they provide a large density of spins and can, therefore, operate at relatively high powers. While solid-state maser oscillators have been demonstrated at room temperature, continuous-wave amplification in these systems has only ever been realized at cryogenic temperatures. Here, we report on a continuous-wave solid-state maser amplifier operating at room temperature. We achieve this feat using a practical setup that includes an ensemble of nitrogen-vacancy center spins in a diamond crystal, a strong permanent magnet, and a simple laser diode. We describe important amplifier characteristics including gain, bandwidth, compression power, and noise temperature and discuss the prospects of realizing a room-temperature near-quantum-noise-limited amplifier with this system. Finally, we show that in a different mode of operation the spins can be used to reduce the microwave noise in an external circuit to cryogenic levels, all without the requirement for physical cooling. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"12 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142848915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-18DOI: 10.1103/physrevx.14.041067
Giovanni Del Monte, Emanuela Zaccarelli
We perform extensive molecular dynamics simulations of an ensemble of realistic microgel particles in swollen conditions in a wide range of packing fractions ζ. We compare neutral and charged microgels, where we consider charge distribution adherent to experimental conditions. Through a detailed analysis of single-particle behavior, we are able to identify the different regimes occurring upon increasing concentration: from shrinking to deformation and interpenetration, always connecting our findings with available experimental observations. We then link these single-particle features with the collective behavior of the suspension, finding evidence of a structural reentrance that has no counterpart in the dynamics. Hence, while the maximum of the radial distribution function displays a nonmonotonic behavior with increasing ζ, the dynamics, quantified by the microgels’ mean-squared displacement, always slows down. This behavior, at odds with the simple Hertzian model, can be described by a phenomenological multi-Hertzian model, which takes into account the enhanced internal stiffness of the core. However, also this model fails when deformation enters into play, whereby more realistic many-body models are required. Thanks to our analysis, we are able to unveil the key physical mechanisms, shrinking and deformation, giving rise to the structural reentrance that holds up to very large packing fractions. We further identify key similarities and differences between neutral and charged microgels, for which we detect at high enough ζ the fusion of charged shells, previously invoked to explain key experimental findings, and responsible for the structural reentrance. Overall, our study establishes a powerful framework to uncover the physics of microgel suspensions, paving the way to tackle different regimes, e.g., high temperature, and internal architectures, such as for hollow and ultralow-cross-linked microgels, where experimental evidence is still limited. Published by the American Physical Society2024
{"title":"Numerical Study of Neutral and Charged Microgel Suspensions: From Single-Particle to Collective Behavior","authors":"Giovanni Del Monte, Emanuela Zaccarelli","doi":"10.1103/physrevx.14.041067","DOIUrl":"https://doi.org/10.1103/physrevx.14.041067","url":null,"abstract":"We perform extensive molecular dynamics simulations of an ensemble of realistic microgel particles in swollen conditions in a wide range of packing fractions ζ</a:mi></a:math>. We compare neutral and charged microgels, where we consider charge distribution adherent to experimental conditions. Through a detailed analysis of single-particle behavior, we are able to identify the different regimes occurring upon increasing concentration: from shrinking to deformation and interpenetration, always connecting our findings with available experimental observations. We then link these single-particle features with the collective behavior of the suspension, finding evidence of a structural reentrance that has no counterpart in the dynamics. Hence, while the maximum of the radial distribution function displays a nonmonotonic behavior with increasing <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>ζ</c:mi></c:math>, the dynamics, quantified by the microgels’ mean-squared displacement, always slows down. This behavior, at odds with the simple Hertzian model, can be described by a phenomenological multi-Hertzian model, which takes into account the enhanced internal stiffness of the core. However, also this model fails when deformation enters into play, whereby more realistic many-body models are required. Thanks to our analysis, we are able to unveil the key physical mechanisms, shrinking and deformation, giving rise to the structural reentrance that holds up to very large packing fractions. We further identify key similarities and differences between neutral and charged microgels, for which we detect at high enough <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mi>ζ</e:mi></e:math> the fusion of charged shells, previously invoked to explain key experimental findings, and responsible for the structural reentrance. Overall, our study establishes a powerful framework to uncover the physics of microgel suspensions, paving the way to tackle different regimes, e.g., high temperature, and internal architectures, such as for hollow and ultralow-cross-linked microgels, where experimental evidence is still limited. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"115 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142848905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-13DOI: 10.1103/physrevx.14.040501
M. Mitrano, S. Johnston, Young-June Kim, M. P. M. Dean
Understanding quantum materials—solids in which interactions among constituent electrons yield a great variety of novel emergent quantum phenomena—is a forefront challenge in modern condensed matter physics. This goal has driven the invention and refinement of several experimental methods, which can spectroscopically determine the elementary excitations and correlation functions that determine material properties. Here we focus on the future experimental and theoretical trends of resonant inelastic x-ray scattering (RIXS), which is a remarkably versatile and rapidly growing technique for probing different charge, lattice, spin, and orbital excitations in quantum materials. We provide a forward-looking introduction to RIXS and outline how this technique is poised to deepen our insight into the nature of quantum materials and of their emergent electronic phenomena. Published by the American Physical Society2024
理解量子材料--其中各组成电子之间的相互作用产生了大量新出现的量子现象的固体--是现代凝聚态物理学的一项前沿挑战。这一目标推动了多种实验方法的发明和改进,这些方法可以通过光谱测定决定材料特性的基本激发和相关函数。共振非弹性 X 射线散射(RIXS)是一种用途广泛、发展迅速的技术,用于探测量子材料中不同的电荷、晶格、自旋和轨道激发。我们对 RIXS 进行了前瞻性的介绍,并概述了这项技术将如何加深我们对量子材料性质及其新出现的电子现象的洞察。 美国物理学会出版 2024
{"title":"Exploring Quantum Materials with Resonant Inelastic X-Ray Scattering","authors":"M. Mitrano, S. Johnston, Young-June Kim, M. P. M. Dean","doi":"10.1103/physrevx.14.040501","DOIUrl":"https://doi.org/10.1103/physrevx.14.040501","url":null,"abstract":"Understanding quantum materials—solids in which interactions among constituent electrons yield a great variety of novel emergent quantum phenomena—is a forefront challenge in modern condensed matter physics. This goal has driven the invention and refinement of several experimental methods, which can spectroscopically determine the elementary excitations and correlation functions that determine material properties. Here we focus on the future experimental and theoretical trends of resonant inelastic x-ray scattering (RIXS), which is a remarkably versatile and rapidly growing technique for probing different charge, lattice, spin, and orbital excitations in quantum materials. We provide a forward-looking introduction to RIXS and outline how this technique is poised to deepen our insight into the nature of quantum materials and of their emergent electronic phenomena. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"29 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142820692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-13DOI: 10.1103/physrevx.14.041065
Pengyuan Shi, Xiaoyu Wang, Lihao Zhang, Wenqin Song, Kunlin Yang, Shuxi Wang, Ruisheng Zhang, Liangliang Zhang, Takashi Taniguchi, Kenji Watanabe, Sen Yang, Lei Zhang, Lei Wang, Wu Shi, Jie Pan, Zhe Wang
Magnetoresistance (MR) oscillations serve as a hallmark of intrinsic quantum behavior, traditionally observed only in conducting systems. Here we report the discovery of MR oscillations in an insulating system, the vertical junctions of CrPS4 which is a two-dimensional A-type antiferromagnetic semiconductor. Systematic investigations of MR peaks under varying conditions, including electrode materials, magnetic field direction, temperature, voltage bias, and layer number, elucidate a correlation between MR oscillations and spin-canted states in CrPS4. Experimental data and analysis point out the important role of the in-gap electronic states in generating MR oscillations, and we propose that spin selected interlayer hopping of localized defect states may be responsible for it. Our findings not only illuminate the unusual electronic transport in CrPS4 but also underscore the potential of van der Waals magnets for exploring interesting phenomena. Published by the American Physical Society2024
{"title":"Magnetoresistance Oscillations in Vertical Junctions of 2D Antiferromagnetic Semiconductor CrPS4","authors":"Pengyuan Shi, Xiaoyu Wang, Lihao Zhang, Wenqin Song, Kunlin Yang, Shuxi Wang, Ruisheng Zhang, Liangliang Zhang, Takashi Taniguchi, Kenji Watanabe, Sen Yang, Lei Zhang, Lei Wang, Wu Shi, Jie Pan, Zhe Wang","doi":"10.1103/physrevx.14.041065","DOIUrl":"https://doi.org/10.1103/physrevx.14.041065","url":null,"abstract":"Magnetoresistance (MR) oscillations serve as a hallmark of intrinsic quantum behavior, traditionally observed only in conducting systems. Here we report the discovery of MR oscillations in an insulating system, the vertical junctions of CrPS</a:mi></a:mrow>4</a:mn></a:mrow></a:msub></a:mrow></a:math> which is a two-dimensional <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:mi>A</c:mi></c:math>-type antiferromagnetic semiconductor. Systematic investigations of MR peaks under varying conditions, including electrode materials, magnetic field direction, temperature, voltage bias, and layer number, elucidate a correlation between MR oscillations and spin-canted states in <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:mrow><e:msub><e:mrow><e:mi>CrPS</e:mi></e:mrow><e:mrow><e:mn>4</e:mn></e:mrow></e:msub></e:mrow></e:math>. Experimental data and analysis point out the important role of the in-gap electronic states in generating MR oscillations, and we propose that spin selected interlayer hopping of localized defect states may be responsible for it. Our findings not only illuminate the unusual electronic transport in <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:mrow><g:msub><g:mrow><g:mi>CrPS</g:mi></g:mrow><g:mrow><g:mn>4</g:mn></g:mrow></g:msub></g:mrow></g:math> but also underscore the potential of van der Waals magnets for exploring interesting phenomena. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2024</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"243 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142820862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}