Pub Date : 2024-06-07DOI: 10.1103/physrevx.14.021040
Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen
A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases—of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by symmetry gives rise to anomalous LRE upon measuring -charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and we uncover the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way.
{"title":"Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases","authors":"Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, Ruben Verresen","doi":"10.1103/physrevx.14.021040","DOIUrl":"https://doi.org/10.1103/physrevx.14.021040","url":null,"abstract":"A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases—of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn></msub></math> Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>G</mi><mo>×</mo><mi>H</mi></math> symmetry gives rise to anomalous LRE upon measuring <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>G</mi></math>-charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and we uncover the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141292670","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 : 2024-06-06DOI: 10.1103/physrevx.14.021039
Jérôme Garnier-Brun, Michael Benzaquen, Jean-Philippe Bouchaud
As a schematic model of the complexity economic agents are confronted with, we introduce the “Sherrington-Kirkpatrick game,” a discrete time binary choice model inspired from mean-field spin glasses. We show that, even in a completely static environment, agents are unable to learn collectively optimal strategies. This is either because the learning process gets trapped in a suboptimal fixed point or because learning never converges and leads to a never-ending evolution of agent intentions. Contrarily to the hope that learning might save the standard “rational expectation” framework in economics, we argue that complex situations are generically unlearnable and agents must do with satisficing solutions, as argued long ago by Simon [Q. J. Econ.69, 99 (1955)]. Only a centralized, omniscient agent endowed with enormous computing power could qualify to determine the optimal strategy of all agents. Using a mix of analytical arguments and numerical simulations, we find that (i) long memory of past rewards is beneficial to learning, whereas overreaction to recent past is detrimental and leads to cycles or chaos; (ii) increased competition (nonreciprocity) destabilizes fixed points and leads first to chaos and, in the high competition limit, to quasicycles; (iii) some amount of randomness in the learning process, perhaps paradoxically, allows the system to reach better collective decisions; (iv) nonstationary, “aging” behavior spontaneously emerges in a large swath of parameter space of our complex but static world. On the positive side, we find that the learning process allows cooperative systems to coordinate around satisficing solutions with rather high (but markedly suboptimal) average reward. However, hypersensitivity to the game parameters makes it impossible to predict ex ante who will be better or worse off in our stylized economy. The statistical description of the space of satisficing solutions is an open problem.
{"title":"Unlearnable Games and “Satisficing” Decisions: A Simple Model for a Complex World","authors":"Jérôme Garnier-Brun, Michael Benzaquen, Jean-Philippe Bouchaud","doi":"10.1103/physrevx.14.021039","DOIUrl":"https://doi.org/10.1103/physrevx.14.021039","url":null,"abstract":"As a schematic model of the complexity economic agents are confronted with, we introduce the “Sherrington-Kirkpatrick game,” a discrete time binary choice model inspired from mean-field spin glasses. We show that, even in a completely static environment, agents are unable to learn collectively optimal strategies. This is either because the learning process gets trapped in a suboptimal fixed point or because learning never converges and leads to a never-ending evolution of agent intentions. Contrarily to the hope that learning might save the standard “rational expectation” framework in economics, we argue that complex situations are generically <i>unlearnable</i> and agents must do with <i>satisficing</i> solutions, as argued long ago by Simon [<span>Q. J. Econ.</span> <b>69</b>, 99 (1955)]. Only a centralized, omniscient agent endowed with enormous computing power could qualify to determine the optimal strategy of all agents. Using a mix of analytical arguments and numerical simulations, we find that (i) long memory of past rewards is beneficial to learning, whereas overreaction to recent past is detrimental and leads to cycles or chaos; (ii) increased competition (nonreciprocity) destabilizes fixed points and leads first to chaos and, in the high competition limit, to quasicycles; (iii) some amount of randomness in the learning process, perhaps paradoxically, allows the system to reach better collective decisions; (iv) nonstationary, “aging” behavior spontaneously emerges in a large swath of parameter space of our complex but static world. On the positive side, we find that the learning process allows cooperative systems to coordinate around satisficing solutions with rather high (but markedly suboptimal) average reward. However, hypersensitivity to the game parameters makes it impossible to predict <i>ex ante</i> who will be better or worse off in our stylized economy. The statistical description of the space of satisficing solutions is an open problem.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141264990","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 : 2024-06-05DOI: 10.1103/physrevx.14.021038
Josefine Enkner, Lorenzo Graziotto, Felice Appugliese, Vasil Rokaj, Jie Wang, Michael Ruggenthaler, Christian Reichl, Werner Wegscheider, Angel Rubio, Jérôme Faist
The value of fundamental physical constants is affected by the coupling of matter to the electromagnetic vacuum state, as predicted and explained by quantum electrodynamics. In this work, we present a millikelvin magnetotransport experiment in the quantum Hall regime that assesses the possibility of the von Klitzing constant being modified by strong cavity vacuum fields. By employing a Wheatstone bridge, we measure the difference between the quantized Hall resistance of a cavity-embedded Hall bar and the resistance standard, achieving an accuracy down to one part in for the lowest Landau level. While our results do not suggest any deviation that could imply a modified Hall resistance, our work represents pioneering efforts in exploring the fundamental implications of vacuum fields in solid-state systems.
{"title":"Testing the Renormalization of the von Klitzing Constant by Cavity Vacuum Fields","authors":"Josefine Enkner, Lorenzo Graziotto, Felice Appugliese, Vasil Rokaj, Jie Wang, Michael Ruggenthaler, Christian Reichl, Werner Wegscheider, Angel Rubio, Jérôme Faist","doi":"10.1103/physrevx.14.021038","DOIUrl":"https://doi.org/10.1103/physrevx.14.021038","url":null,"abstract":"The value of fundamental physical constants is affected by the coupling of matter to the electromagnetic vacuum state, as predicted and explained by quantum electrodynamics. In this work, we present a millikelvin magnetotransport experiment in the quantum Hall regime that assesses the possibility of the von Klitzing constant being modified by strong cavity vacuum fields. By employing a Wheatstone bridge, we measure the difference between the quantized Hall resistance of a cavity-embedded Hall bar and the resistance standard, achieving an accuracy down to one part in <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mn>5</mn></msup></math> for the lowest Landau level. While our results do not suggest any deviation that could imply a modified Hall resistance, our work represents pioneering efforts in exploring the fundamental implications of vacuum fields in solid-state systems.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141264844","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 : 2024-06-04DOI: 10.1103/physrevx.14.021037
Andreas Morr, Niklas Boers
Detection of critical slowing down (CSD) is the dominant avenue for anticipating critical transitions from noisy time-series data. Most commonly, changes in variance and lag-1 autocorrelation [AC(1)] are used as CSD indicators. However, these indicators will only produce reliable results if the noise driving the system is white and stationary. In the more realistic case of time-correlated red noise, increasing (decreasing) the correlation of the noise will lead to spurious (masked) alarms for both variance and AC(1). Here, we propose two new methods that can discriminate true CSD from possible changes in the driving noise characteristics. We focus on estimating changes in the linear restoring rate based on Langevin-type dynamics driven by either white or red noise. We assess the capacity of our new estimators to anticipate critical transitions and show that they perform significantly better than other existing methods both for continuous-time and discrete-time models. In addition to conceptual models, we apply our methods to climate model simulations of the termination of the African Humid Period. The estimations rule out spurious signals stemming from nonstationary noise characteristics and reveal a destabilization of the African climate system as the dynamical mechanism underlying this archetype of abrupt climate change in the past.
{"title":"Detection of Approaching Critical Transitions in Natural Systems Driven by Red Noise","authors":"Andreas Morr, Niklas Boers","doi":"10.1103/physrevx.14.021037","DOIUrl":"https://doi.org/10.1103/physrevx.14.021037","url":null,"abstract":"Detection of critical slowing down (CSD) is the dominant avenue for anticipating critical transitions from noisy time-series data. Most commonly, changes in variance and lag-1 autocorrelation [AC(1)] are used as CSD indicators. However, these indicators will only produce reliable results if the noise driving the system is white and stationary. In the more realistic case of time-correlated red noise, increasing (decreasing) the correlation of the noise will lead to spurious (masked) alarms for both variance and AC(1). Here, we propose two new methods that can discriminate true CSD from possible changes in the driving noise characteristics. We focus on estimating changes in the linear restoring rate based on Langevin-type dynamics driven by either white or red noise. We assess the capacity of our new estimators to anticipate critical transitions and show that they perform significantly better than other existing methods both for continuous-time and discrete-time models. In addition to conceptual models, we apply our methods to climate model simulations of the termination of the African Humid Period. The estimations rule out spurious signals stemming from nonstationary noise characteristics and reveal a destabilization of the African climate system as the dynamical mechanism underlying this archetype of abrupt climate change in the past.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141246485","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 : 2024-06-03DOI: 10.1103/physrevx.14.021036
Anton Bochkarev, Yury Lysogorskiy, Ralf Drautz
The atomic cluster expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the atomic cluster expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph atomic cluster expansion for a number of small molecules, clusters, and a general-purpose model for carbon. We further show that the graph atomic cluster expansion scales linearly with the number of neighbors and layer depth of the graph basis functions.
{"title":"Graph Atomic Cluster Expansion for Semilocal Interactions beyond Equivariant Message Passing","authors":"Anton Bochkarev, Yury Lysogorskiy, Ralf Drautz","doi":"10.1103/physrevx.14.021036","DOIUrl":"https://doi.org/10.1103/physrevx.14.021036","url":null,"abstract":"The atomic cluster expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the atomic cluster expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph atomic cluster expansion for a number of small molecules, clusters, and a general-purpose model for carbon. We further show that the graph atomic cluster expansion scales linearly with the number of neighbors and layer depth of the graph basis functions.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141246641","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 : 2024-05-30DOI: 10.1103/physrevx.14.021035
S. Popa, S. Schaller, A. Fielicke, J. Lim, B. G. Sartakov, M. R. Tarbutt, G. Meijer
Molecules containing a lanthanide atom have sets of electronic states arising from excitation of an inner-shell electron. These states have received little attention but are thought to play an important role in laser cooling of such molecules and may be a useful resource for testing fundamental physics. We study a series of inner-shell excited states in YbF using resonance-enhanced multiphoton ionization spectroscopy. We investigate the excited states of lowest energy, 8474, 9013, and above the ground state, all corresponding to the configuration of the ion. They are metastable, since they have no electric dipole allowed transitions to the ground state. We also characterize a state at that is easily excited from both the ground and metastable states, which makes it especially useful for this spectroscopic study. Finally, we study two states at 48 720 and , which are above the ionization limit and feature strong autoionizing resonances that prove useful for efficient detection of the molecules and for identifying the rotational quantum number of each line in the spectrum. We resolve the rotational structures of all these states and find that they can all be described by a very simple model based on Hund’s case (c). Our study provides information necessary for laser slowing and magneto-optical trapping of YbF, which is an important species for testing fundamental physics. We also consider whether the low-lying inner-shell states may themselves be useful as probes of the electron’s electric dipole moment or of varying fundamental constants, since they are long-lived states in a laser-coolable molecule featuring closely spaced levels of opposite parity.
{"title":"Understanding Inner-Shell Excitations in Molecules through Spectroscopy of the 4f Hole States of YbF","authors":"S. Popa, S. Schaller, A. Fielicke, J. Lim, B. G. Sartakov, M. R. Tarbutt, G. Meijer","doi":"10.1103/physrevx.14.021035","DOIUrl":"https://doi.org/10.1103/physrevx.14.021035","url":null,"abstract":"Molecules containing a lanthanide atom have sets of electronic states arising from excitation of an inner-shell electron. These states have received little attention but are thought to play an important role in laser cooling of such molecules and may be a useful resource for testing fundamental physics. We study a series of inner-shell excited states in YbF using resonance-enhanced multiphoton ionization spectroscopy. We investigate the excited states of lowest energy, 8474, 9013, and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>9090</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> above the ground state, all corresponding to the configuration <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>4</mn><msup><mrow><mi>f</mi></mrow><mrow><mn>13</mn></mrow></msup><mn>6</mn><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msub><mrow><mmultiscripts><mrow><mi>F</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow><mrow><mn>7</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></math> of the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mrow><mi>Yb</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> ion. They are metastable, since they have no electric dipole allowed transitions to the ground state. We also characterize a state at <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>31</mn><mtext> </mtext><mn>050</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> that is easily excited from both the ground and metastable states, which makes it especially useful for this spectroscopic study. Finally, we study two states at 48 720 and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>48</mn><mtext> </mtext><mn>729</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, which are above the ionization limit and feature strong autoionizing resonances that prove useful for efficient detection of the molecules and for identifying the rotational quantum number of each line in the spectrum. We resolve the rotational structures of all these states and find that they can all be described by a very simple model based on Hund’s case (c). Our study provides information necessary for laser slowing and magneto-optical trapping of YbF, which is an important species for testing fundamental physics. We also consider whether the low-lying inner-shell states may themselves be useful as probes of the electron’s electric dipole moment or of varying fundamental constants, since they are long-lived states in a laser-coolable molecule featuring closely spaced levels of opposite parity.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182500","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 : 2024-05-29DOI: 10.1103/physrevx.14.021034
Shankar Balasubramanian, Sarang Gopalakrishnan, Alexey Khudorozhkov, Ethan Lake
We introduce a family of local models of dynamics based on “word problems” from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must “work out” the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic but can be made ergodic by appending a large reservoir of sites in a trivial product state. This finding manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wave vector exhibit almost no relaxation until times , at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions.
{"title":"Glassy Word Problems: Ultraslow Relaxation, Hilbert Space Jamming, and Computational Complexity","authors":"Shankar Balasubramanian, Sarang Gopalakrishnan, Alexey Khudorozhkov, Ethan Lake","doi":"10.1103/physrevx.14.021034","DOIUrl":"https://doi.org/10.1103/physrevx.14.021034","url":null,"abstract":"We introduce a family of local models of dynamics based on “word problems” from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must “work out” the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic but can be made ergodic by appending a large reservoir of sites in a trivial product state. This finding manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wave vector <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>q</mi></math> exhibit almost no relaxation until times <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>O</mi><mo mathvariant=\"bold\" stretchy=\"false\">(</mo><mi>exp</mi><mo stretchy=\"false\">(</mo><mn>1</mn><mo>/</mo><mi>q</mi><mo stretchy=\"false\">)</mo><mo mathvariant=\"bold\" stretchy=\"false\">)</mo></mrow></math>, at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141177473","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 : 2024-05-28DOI: 10.1103/physrevx.14.021033
Sophie F. Weber, Andrea Urru, Sayantika Bhowal, Claude Ederer, Nicola A. Spaldin
We use symmetry analysis and density-functional theory to determine and characterize surface terminations that have a finite equilibrium magnetization density in antiferromagnetic materials. A nonzero magnetic dipole moment per unit area or “surface magnetization” can arise on particular surfaces of many antiferromagnets due to the bulk magnetic symmetries. Such surface magnetization underlies intriguing physical phenomena like interfacial magnetic coupling and can be used as a readout method of antiferromagnetic domains. However, a universal description of antiferromagnetic surface magnetization is lacking. We first introduce a classification system based on whether the surface magnetization is either sensitive or robust to roughness and on whether the magnetic dipoles at surface of interest are compensated or uncompensated when the bulk magnetic order is retained at the surface. We show that roughness-sensitive categories can be identified by a simple extension of a previously established group-theory formalism for identifying roughness-robust surface magnetization. We then map the group-theory method of identifying surface magnetization to a novel description in terms of bulk magnetic multipoles, which are already established as symmetry indicators for bulk magnetoelectric responses at both linear and higher orders. We use density-functional calculations to illustrate that nominally compensated surfaces in magnetoelectric and centrosymmetric altermagnetic develop a finite magnetization density at the surface, in agreement with our predictions based on both group theory and the ordering of the bulk multipoles. Our analysis provides a comprehensive basis for understanding the surface magnetic properties and their intimate correspondence to bulk magnetoelectric effects in antiferromagnets and has important implications for technologically relevant phenomena such as exchange-bias coupling.
{"title":"Surface Magnetization in Antiferromagnets: Classification, Example Materials, and Relation to Magnetoelectric Responses","authors":"Sophie F. Weber, Andrea Urru, Sayantika Bhowal, Claude Ederer, Nicola A. Spaldin","doi":"10.1103/physrevx.14.021033","DOIUrl":"https://doi.org/10.1103/physrevx.14.021033","url":null,"abstract":"We use symmetry analysis and density-functional theory to determine and characterize surface terminations that have a finite equilibrium magnetization density in antiferromagnetic materials. A nonzero magnetic dipole moment per unit area or “surface magnetization” can arise on particular surfaces of many antiferromagnets due to the bulk magnetic symmetries. Such surface magnetization underlies intriguing physical phenomena like interfacial magnetic coupling and can be used as a readout method of antiferromagnetic domains. However, a universal description of antiferromagnetic surface magnetization is lacking. We first introduce a classification system based on whether the surface magnetization is either sensitive or robust to roughness and on whether the magnetic dipoles at surface of interest are compensated or uncompensated when the bulk magnetic order is retained at the surface. We show that roughness-sensitive categories can be identified by a simple extension of a previously established group-theory formalism for identifying roughness-robust surface magnetization. We then map the group-theory method of identifying surface magnetization to a novel description in terms of bulk magnetic multipoles, which are already established as symmetry indicators for bulk magnetoelectric responses at both linear and higher orders. We use density-functional calculations to illustrate that nominally compensated surfaces in magnetoelectric <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi>Cr</mi></mrow><mn>2</mn></msub><msub><mrow><mi mathvariant=\"normal\">O</mi></mrow><mn>3</mn></msub></mrow></math> and centrosymmetric altermagnetic <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi>FeF</mi></mrow><mn>2</mn></msub></mrow></math> develop a finite magnetization density at the surface, in agreement with our predictions based on both group theory and the ordering of the bulk multipoles. Our analysis provides a comprehensive basis for understanding the surface magnetic properties and their intimate correspondence to bulk magnetoelectric effects in antiferromagnets and has important implications for technologically relevant phenomena such as exchange-bias coupling.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141159474","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 : 2024-05-24DOI: 10.1103/physrevx.14.021032
Sarah A. M. Loos, Samuel Monter, Felix Ginot, Clemens Bechinger
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here, we experimentally and theoretically investigate the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimized. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.
{"title":"Universal Symmetry of Optimal Control at the Microscale","authors":"Sarah A. M. Loos, Samuel Monter, Felix Ginot, Clemens Bechinger","doi":"10.1103/physrevx.14.021032","DOIUrl":"https://doi.org/10.1103/physrevx.14.021032","url":null,"abstract":"Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here, we experimentally and theoretically investigate the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimized. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091786","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 : 2024-05-24DOI: 10.1103/physrevx.14.021031
Simon Yves, Emanuele Galiffi, Xiang Ni, Enrico M. Renzi, Andrea Alù
Following the discovery of moiré-driven superconductivity and density waves in twisted-graphene multilayers, twistronics has spurred a surge of interest in tailored broken symmetries through angular rotations enabling new properties, from electronics to photonics and phononics. Analogously, in monoclinic polar crystals a nontrivial angle between nondegenerate dipolar phonon resonances can naturally emerge due to asymmetries in their crystal lattice, and its variations are associated with intriguing polaritonic phenomena, including axial dispersion, i.e., the rotation of the optical axis with frequency, and microscopic shear effects that result in an asymmetric distribution of material loss. So far, these phenomena have been restricted to specific midinfrared frequencies difficult to access with conventional laser sources and fundamentally limited by the degree of asymmetry and by the strength of light-matter interactions available in natural crystals. Here, we leverage the twistronics concept to demonstrate maximal axial dispersion and loss redistribution of hyperbolic waves in elastic metasurfaces, achieved by tailoring the angle between coupled metasurface pairs featuring tailored anisotropy. We show extreme control over elastic wave dispersion and absorption via the twist angle and leverage the resulting phenomena to demonstrate enhanced propagation distance, in-plane reflection-free negative refraction and diffraction-free defect detection. Our work welds the concepts of twistronics, non-Hermiticity, and extreme anisotropy, demonstrating the powerful opportunities enabled by metasurfaces for tunable, highly directional surface-acoustic-wave propagation of great interest for a wide range of applications spanning from seismic mitigation to on-chip phononics and wireless communication systems, hence paving the way toward their translation into emerging photonic and polaritonic metasurface technologies.
{"title":"Twist-Induced Hyperbolic Shear Metasurfaces","authors":"Simon Yves, Emanuele Galiffi, Xiang Ni, Enrico M. Renzi, Andrea Alù","doi":"10.1103/physrevx.14.021031","DOIUrl":"https://doi.org/10.1103/physrevx.14.021031","url":null,"abstract":"Following the discovery of moiré-driven superconductivity and density waves in twisted-graphene multilayers, twistronics has spurred a surge of interest in tailored broken symmetries through angular rotations enabling new properties, from electronics to photonics and phononics. Analogously, in monoclinic polar crystals a nontrivial angle between nondegenerate dipolar phonon resonances can naturally emerge due to asymmetries in their crystal lattice, and its variations are associated with intriguing polaritonic phenomena, including axial dispersion, i.e., the rotation of the optical axis with frequency, and microscopic shear effects that result in an asymmetric distribution of material loss. So far, these phenomena have been restricted to specific midinfrared frequencies difficult to access with conventional laser sources and fundamentally limited by the degree of asymmetry and by the strength of light-matter interactions available in natural crystals. Here, we leverage the twistronics concept to demonstrate maximal axial dispersion and loss redistribution of hyperbolic waves in elastic metasurfaces, achieved by tailoring the angle between coupled metasurface pairs featuring tailored anisotropy. We show extreme control over elastic wave dispersion and absorption via the twist angle and leverage the resulting phenomena to demonstrate enhanced propagation distance, in-plane reflection-free negative refraction and diffraction-free defect detection. Our work welds the concepts of twistronics, non-Hermiticity, and extreme anisotropy, demonstrating the powerful opportunities enabled by metasurfaces for tunable, highly directional surface-acoustic-wave propagation of great interest for a wide range of applications spanning from seismic mitigation to on-chip phononics and wireless communication systems, hence paving the way toward their translation into emerging photonic and polaritonic metasurface technologies.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091778","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}
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