Pub Date : 2024-06-11DOI: 10.1103/physrevx.14.021043
Y.-F. Li, S.-D. Chen, M. García-Díez, M. I. Iraola, H. Pfau, Y.-L. Zhu, Z.-Q. Mao, T. Chen, M. Yi, P.-C. Dai, J. A. Sobota, M. Hashimoto, M. G. Vergniory, D.-H. Lu, Z.-X. Shen
(FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial due to the band inversion between the and bands along . However, there remain debates in both the authenticity of the Dirac surface states (DSSs) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive angle-resolved photoemission spectroscopy investigation. We first observe a persistent DSS independent of . Then, by comparing FTS with FeSe, which has no band inversion along , we identify the spectral weight fingerprint of both the presence of the band and the inversion between the and bands. Furthermore, we propose a renormalization scheme for the band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor.
{"title":"Orbital Ingredients and Persistent Dirac Surface State for the Topological Band Structure in FeTe0.55Se0.45","authors":"Y.-F. Li, S.-D. Chen, M. García-Díez, M. I. Iraola, H. Pfau, Y.-L. Zhu, Z.-Q. Mao, T. Chen, M. Yi, P.-C. Dai, J. A. Sobota, M. Hashimoto, M. G. Vergniory, D.-H. Lu, Z.-X. Shen","doi":"10.1103/physrevx.14.021043","DOIUrl":"https://doi.org/10.1103/physrevx.14.021043","url":null,"abstract":"<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>FeTe</mi><mn>0.55</mn></msub><mrow><msub><mrow><mi>Se</mi></mrow><mrow><mn>0.45</mn></mrow></msub></mrow></math> (FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial due to the band inversion between the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>d</mi><mrow><mi>x</mi><mi>z</mi></mrow></msub></math> and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>p</mi><mi>z</mi></msub></math> bands along <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">Γ</mi><mtext>−</mtext><mi>Z</mi></mrow></math>. However, there remain debates in both the authenticity of the Dirac surface states (DSSs) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive angle-resolved photoemission spectroscopy investigation. We first observe a persistent DSS independent of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>k</mi><mi>z</mi></msub></math>. Then, by comparing FTS with FeSe, which has no band inversion along <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">Γ</mi><mtext>−</mtext><mi>Z</mi></mrow></math>, we identify the spectral weight fingerprint of both the presence of the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>p</mi><mi>z</mi></msub></math> band and the inversion between the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>d</mi><mrow><mi>x</mi><mi>z</mi></mrow></msub></math> and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>p</mi><mi>z</mi></msub></math> bands. Furthermore, we propose a renormalization scheme for the band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"1 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141309036","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 : 2024-06-10DOI: 10.1103/physrevx.14.021042
Xiaoyu Wang, Oskar Vafek
Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number for , , , and . We also find correlated Chern insulators at unconventional sequences with , as well as with fractional , and elucidate their nature.
魔角扭曲双层石墨烯是研究得最透彻的物理平台，其特点是摩尔势诱导的窄带具有非难拓扑和强电子相关性。尽管其重要性不言而喻，但在有限磁场下观察到的切尔诺绝缘态--推断为零磁场下的带填充态--仍然鲜为人知。揭示其本质是摩尔材料领域最重要的未决问题之一。在此，我们首次对有限磁场中的相互作用电子进行了全面研究，同时改变了电子密度、扭转角和异应变。在扭转角范围内出现的一系列相关切尔恩相中，我们发现了一个统一的描述，即在(s,t)=±(0,4)、±(1,3)、±(2,2)和±(3,1)时，切尔恩数为 t 的无处不在的状态序列。我们还在 s+t≠±4 以及分数 s 的非常规序列中发现了相关的切尔诺绝缘体，并阐明了它们的性质。
{"title":"Theory of Correlated Chern Insulators in Twisted Bilayer Graphene","authors":"Xiaoyu Wang, Oskar Vafek","doi":"10.1103/physrevx.14.021042","DOIUrl":"https://doi.org/10.1103/physrevx.14.021042","url":null,"abstract":"Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>s</mi></math> at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi></math> for <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mo>±</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>4</mn><mo stretchy=\"false\">)</mo></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mo stretchy=\"false\">(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mo stretchy=\"false\">(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo stretchy=\"false\">)</mo></math>, and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>±</mo><mo stretchy=\"false\">(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math>. We also find correlated Chern insulators at unconventional sequences with <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>s</mi><mo>+</mo><mi>t</mi><mo>≠</mo><mo>±</mo><mn>4</mn></math>, as well as with fractional <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>s</mi></math>, and elucidate their nature.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"33 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304546","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 : 2024-06-10DOI: 10.1103/physrevx.14.021041
Malte Brammerloh, Renat Sibgatulin, Karl-Heinz Herrmann, Markus Morawski, Tilo Reinert, Carsten Jäger, Roland Müller, Gerald Falkenberg, Dennis Brückner, Kerrin J. Pine, Andreas Deistung, Valerij G. Kiselev, Jürgen R. Reichenbach, Nikolaus Weiskopf, Evgeniya Kirilina
Paramagnetic transition metals play a crucial role as cofactors in various cellular catalytic processes. However, their high concentrations in reactive oxidation states can induce oxidative stress, resulting in cell dysfunction or death. Hence, it is vital to have methods to monitor metal concentrations and paramagnetic properties in cells for medicine and cell biology. Here we present a novel multimodal method for in-cell magnetometry enabling direct measurement of metal magnetic properties within individual cells in tissue, without prior isolation and at room temperature. Individual cell magnetic moments are measured using superresolution magnetic resonance imaging (MRI) microscopy at 9.4 T by detecting microscopic magnetic-field perturbations around the cells. The cellular metal content is quantified using ion-beam microscopy or synchrotron micro-x-ray fluorescence for the same cells. The metal magnetic susceptibility at 9.4 T is then obtained from the slope of the cell magnetic moments’ dependence on cell metal content. To estimate the susceptibility at lower fields, multifield MR relaxometry and biophysical modeling are employed, extrapolating the 9.4-T susceptibility values to fields as low as 3 T. We apply the new method to determine the susceptibility of iron accumulated in human dopaminergic neurons inside neuromelanin, the by-product of dopamine synthesis. The susceptibility of iron in neuromelanin is measured to be providing unique insights into the biochemistry of iron inside dopaminergic neurons. The obtained value reveals a predominant monoatomic low-affinity iron-binding site within neuromelanin, indicating a higher neurotoxicity of iron than previously suggested. Furthermore, the measured susceptibility value establishes a quantitative relationship between cellular iron concentration and iron-sensitive MRI parameters, which can be noninvasively measured in vivo. This breakthrough paves the way for the in vivo detection of dopaminergic neuron density and iron load, requiring a standard clinical MRI scanner only. It promises to facilitate early diagnosis of Parkinson’s disease. In conclusion, our presented novel method enables the direct measurements of magnetic properties of paramagnetic metals within single cells with high sensitivity and across large cell groups within a macroscopic volume, providing invaluable information about the cellular biology of metals.
顺磁性过渡金属在各种细胞催化过程中作为辅助因子发挥着至关重要的作用。然而，它们在反应性氧化状态下的高浓度会诱发氧化应激，导致细胞功能障碍或死亡。因此，拥有监测细胞中金属浓度和顺磁性能的方法对于医学和细胞生物学来说至关重要。在这里，我们提出了一种新颖的多模式细胞内磁力测量方法，无需事先分离，可在室温下直接测量组织中单个细胞内的金属磁性。通过检测细胞周围的微观磁场扰动，在 9.4 T 下使用超分辨率磁共振成像（MRI）显微镜测量单个细胞的磁矩。使用离子束显微镜或同步加速器微 X 射线荧光对相同细胞的细胞金属含量进行量化。然后根据细胞磁矩与细胞金属含量的斜率关系得出 9.4 T 时的金属磁感应强度。为了估算较低磁场下的磁感应强度，我们采用了多场磁共振弛豫测量法和生物物理模型，将 9.4 T 的磁感应强度值外推至低至 3 T 的磁场。测得神经络氨酸中铁的易感性为χρ=(2.98±0.19)×10-6 m3/kg，为了解多巴胺能神经元内铁的生物化学提供了独特的见解。所获得的值揭示了神经髓鞘内一个主要的单原子低亲和性铁结合位点，表明铁的神经毒性比以前认为的要高。此外，所测得的易感度值还确定了细胞铁浓度与铁敏感磁共振成像参数之间的定量关系，这种关系可以在体内进行无创测量。这一突破为在体内检测多巴胺能神经元密度和铁负荷铺平了道路，只需要一台标准的临床磁共振成像扫描仪。它有望促进帕金森病的早期诊断。总之，我们提出的新方法能够以高灵敏度直接测量单细胞内顺磁性金属的磁特性，并在宏观体积内测量大细胞群的磁特性，从而提供有关金属的细胞生物学的宝贵信息。
{"title":"In Situ Magnetometry of Iron in Human Dopaminergic Neurons Using Superresolution MRI and Ion-Beam Microscopy","authors":"Malte Brammerloh, Renat Sibgatulin, Karl-Heinz Herrmann, Markus Morawski, Tilo Reinert, Carsten Jäger, Roland Müller, Gerald Falkenberg, Dennis Brückner, Kerrin J. Pine, Andreas Deistung, Valerij G. Kiselev, Jürgen R. Reichenbach, Nikolaus Weiskopf, Evgeniya Kirilina","doi":"10.1103/physrevx.14.021041","DOIUrl":"https://doi.org/10.1103/physrevx.14.021041","url":null,"abstract":"Paramagnetic transition metals play a crucial role as cofactors in various cellular catalytic processes. However, their high concentrations in reactive oxidation states can induce oxidative stress, resulting in cell dysfunction or death. Hence, it is vital to have methods to monitor metal concentrations and paramagnetic properties in cells for medicine and cell biology. Here we present a novel multimodal method for in-cell magnetometry enabling direct measurement of metal magnetic properties within individual cells in tissue, without prior isolation and at room temperature. Individual cell magnetic moments are measured using superresolution magnetic resonance imaging (MRI) microscopy at 9.4 T by detecting microscopic magnetic-field perturbations around the cells. The cellular metal content is quantified using ion-beam microscopy or synchrotron micro-x-ray fluorescence for the same cells. The metal magnetic susceptibility at 9.4 T is then obtained from the slope of the cell magnetic moments’ dependence on cell metal content. To estimate the susceptibility at lower fields, multifield MR relaxometry and biophysical modeling are employed, extrapolating the 9.4-T susceptibility values to fields as low as 3 T. We apply the new method to determine the susceptibility of iron accumulated in human dopaminergic neurons inside neuromelanin, the by-product of dopamine synthesis. The susceptibility of iron in neuromelanin is measured to be <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>=</mo><mo stretchy=\"false\">(</mo><mn>2.98</mn><mo>±</mo><mn>0.19</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup><mtext> </mtext><mtext> </mtext><msup><mi mathvariant=\"normal\">m</mi><mn>3</mn></msup><mo>/</mo><mi>kg</mi></mrow></math> providing unique insights into the biochemistry of iron inside dopaminergic neurons. The obtained value reveals a predominant monoatomic low-affinity iron-binding site within neuromelanin, indicating a higher neurotoxicity of iron than previously suggested. Furthermore, the measured susceptibility value establishes a quantitative relationship between cellular iron concentration and iron-sensitive MRI parameters, which can be noninvasively measured <i>in vivo</i>. This breakthrough paves the way for the <i>in vivo</i> detection of dopaminergic neuron density and iron load, requiring a standard clinical MRI scanner only. It promises to facilitate early diagnosis of Parkinson’s disease. In conclusion, our presented novel method enables the direct measurements of magnetic properties of paramagnetic metals within single cells with high sensitivity and across large cell groups within a macroscopic volume, providing invaluable information about the cellular biology of metals.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"32 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141304359","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 : 2024-06-07DOI: 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":"30 1","pages":""},"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":"30 1","pages":""},"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":"34 1","pages":""},"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":"12 1","pages":""},"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":"21 1","pages":""},"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":"29 1","pages":""},"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":"8 1","pages":""},"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}
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