Flocking, as paradigmatically exemplified by birds, is the coherent collective motion of active agents. As originally conceived, flocking emerges through alignment interactions between the agents. Here, we report that flocking can also emerge through interactions that turn agents away from each other. Combining simulations, kinetic theory, and experiments, we demonstrate this mechanism of flocking in self-propelled Janus colloids with stronger repulsion on the front than on the rear. The polar state is stable because particles achieve a compromise between turning away from left and right neighbors. Unlike for alignment interactions, the emergence of polar order from turn-away interactions requires particle repulsion. At high concentration, repulsion produces flocking Wigner crystals. Whereas repulsion often leads to motility-induced phase separation of active particles, here it combines with turn-away torques to produce flocking. Therefore, our findings bridge the classes of aligning and nonaligning active matter. Our results could help to reconcile the observations that cells can flock despite turning away from each other via contact inhibition of locomotion. Overall, our work shows that flocking is a very robust phenomenon that arises even when the orientational interactions would seem to prevent it.
{"title":"Flocking by Turning Away","authors":"Suchismita Das, Matteo Ciarchi, Ziqi Zhou, Jing Yan, Jie Zhang, Ricard Alert","doi":"10.1103/physrevx.14.031008","DOIUrl":"https://doi.org/10.1103/physrevx.14.031008","url":null,"abstract":"Flocking, as paradigmatically exemplified by birds, is the coherent collective motion of active agents. As originally conceived, flocking emerges through alignment interactions between the agents. Here, we report that flocking can also emerge through interactions that turn agents away from each other. Combining simulations, kinetic theory, and experiments, we demonstrate this mechanism of flocking in self-propelled Janus colloids with stronger repulsion on the front than on the rear. The polar state is stable because particles achieve a compromise between turning away from left and right neighbors. Unlike for alignment interactions, the emergence of polar order from turn-away interactions requires particle repulsion. At high concentration, repulsion produces flocking Wigner crystals. Whereas repulsion often leads to motility-induced phase separation of active particles, here it combines with turn-away torques to produce flocking. Therefore, our findings bridge the classes of aligning and nonaligning active matter. Our results could help to reconcile the observations that cells can flock despite turning away from each other via contact inhibition of locomotion. Overall, our work shows that flocking is a very robust phenomenon that arises even when the orientational interactions would seem to prevent it.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597275","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 : 2024-07-11DOI: 10.1103/physrevx.14.031006
Jie Wang, Jacopo Surace, Irénée Frérot, Benoît Legat, Marc-Olivier Renou, Victor Magron, Antonio Acín
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalization quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: Energy is minimized over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all that variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of this approach in paradigmatic examples of 1D and 2D spin- Heisenberg models. To improve the scalability of the method, we exploit the symmetries and sparsity of the considered systems to reach sizes of hundreds of particles at much higher precision than previous works. Our analysis therefore shows how to obtain certifiable bounds on many-body ground-state properties beyond energy in a scalable way.
{"title":"Certifying Ground-State Properties of Many-Body Systems","authors":"Jie Wang, Jacopo Surace, Irénée Frérot, Benoît Legat, Marc-Olivier Renou, Victor Magron, Antonio Acín","doi":"10.1103/physrevx.14.031006","DOIUrl":"https://doi.org/10.1103/physrevx.14.031006","url":null,"abstract":"A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalization quickly becomes impossible when increasing the system size, variational approaches are typically employed as a scalable alternative: Energy is minimized over a subset of all possible states and then different physical quantities are computed over the solution state. Despite remarkable success, rigorously speaking, all that variational methods offer are upper bounds on the ground-state energy. On the other hand, so-called relaxations of the ground-state problem based on semidefinite programming represent a complementary approach, providing lower bounds to the ground-state energy. However, in their current implementation, neither variational nor relaxation methods offer provable bound on other observables in the ground state beyond the energy. In this work, we show that the combination of the two classes of approaches can be used to derive certifiable bounds on the value of any observable in the ground state, such as correlation functions of arbitrary order, structure factors, or order parameters. We illustrate the power of this approach in paradigmatic examples of 1D and 2D spin-<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>1</mn><mo>/</mo><mn>2</mn></math> Heisenberg models. To improve the scalability of the method, we exploit the symmetries and sparsity of the considered systems to reach sizes of hundreds of particles at much higher precision than previous works. Our analysis therefore shows how to obtain certifiable bounds on many-body ground-state properties beyond energy in a scalable way.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597277","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 : 2024-07-10DOI: 10.1103/physrevx.14.031005
Shobhna Singh, Jerome Lloyd, Felix Flicker
We provide a simple algorithm for constructing Hamiltonian graph cycles (visiting every vertex exactly once) on a set of arbitrarily large finite subgraphs of aperiodic two-dimensional Ammann-Beenker (AB) tilings. Using this result, and the discrete scale symmetry of AB tilings, we find exact solutions to a range of other problems which lie in the complexity class NP-complete for general graphs. These include the equal-weight traveling salesperson problem, providing, for example, the most efficient route a scanning tunneling microscope tip could take to image the atoms of physical quasicrystals with AB symmetries; the longest path problem, whose solution demonstrates that collections of flexible molecules of any length can adsorb onto AB quasicrystal surfaces at density one, with possible applications to catalysis; and the three-coloring problem, giving ground states for the -state Potts model () of magnetic interactions defined on the planar dual to AB, which may provide useful models for protein folding.
我们提供了一种在一组任意大的有限子图上构建汉密尔顿图循环（每个顶点精确访问一次）的简单算法，这些子图是非周期性的二维安曼-宾克（AB）倾斜图。利用这一结果和 AB 层的离散尺度对称性，我们找到了一系列其他问题的精确解，这些问题的复杂度属于一般图的 NP-完全问题。这些问题包括等权旅行推销员问题，例如，它提供了扫描隧道显微镜尖端对具有 AB 对称性的物理准晶体的原子进行成像的最有效路径；最长路径问题，该问题的求解证明了任何长度的柔性分子集合都能在密度为一的情况下吸附到 AB 类晶体表面，并可能应用于催化作用；以及三着色问题，该问题给出了定义在 AB 平面对偶面上的磁相互作用 q 态波茨模型（q≥3）的基态，这可能为蛋白质折叠提供有用的模型。
{"title":"Hamiltonian Cycles on Ammann-Beenker Tilings","authors":"Shobhna Singh, Jerome Lloyd, Felix Flicker","doi":"10.1103/physrevx.14.031005","DOIUrl":"https://doi.org/10.1103/physrevx.14.031005","url":null,"abstract":"We provide a simple algorithm for constructing Hamiltonian graph cycles (visiting every vertex exactly once) on a set of arbitrarily large finite subgraphs of aperiodic two-dimensional Ammann-Beenker (AB) tilings. Using this result, and the discrete scale symmetry of AB tilings, we find exact solutions to a range of other problems which lie in the complexity class NP-complete for general graphs. These include the equal-weight traveling salesperson problem, providing, for example, the most efficient route a scanning tunneling microscope tip could take to image the atoms of physical quasicrystals with AB symmetries; the longest path problem, whose solution demonstrates that collections of flexible molecules of any length can adsorb onto AB quasicrystal surfaces at density one, with possible applications to catalysis; and the three-coloring problem, giving ground states for the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>q</mi></math>-state Potts model (<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>q</mi><mo>≥</mo><mn>3</mn></math>) of magnetic interactions defined on the planar dual to AB, which may provide useful models for protein folding.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141566071","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}
Interfacing cold atoms with integrated nanophotonic devices could offer new paradigms for engineering atom-light interactions and provide a potentially scalable route for quantum sensing, metrology, and quantum information processing. However, it remains a challenging task to efficiently trap a large ensemble of cold atoms on an integrated nanophotonic circuit. Here, we demonstrate direct loading of an ensemble of up to 70 atoms into an optical microtrap on a nanophotonic microring circuit. Efficient trap loading is achieved by employing degenerate Raman-sideband cooling in the microtrap, where a built-in spin-motion coupling arises directly from the vector light shift of the evanescent-field potential on a microring. Atoms are cooled into the trap via optical pumping with a single free space beam. We have achieved a trap lifetime approaching 700 ms under continuous cooling. We show that the trapped atoms display large cooperative coupling and superradiant decay into a whispering-gallery mode of the microring resonator, holding promise for explorations of new collective effects. Our technique can be extended to trapping a large ensemble of cold atoms on nanophotonic circuits for various quantum applications.
{"title":"Trapped Atoms and Superradiance on an Integrated Nanophotonic Microring Circuit","authors":"Xinchao Zhou, Hikaru Tamura, Tzu-Han Chang, Chen-Lung Hung","doi":"10.1103/physrevx.14.031004","DOIUrl":"https://doi.org/10.1103/physrevx.14.031004","url":null,"abstract":"Interfacing cold atoms with integrated nanophotonic devices could offer new paradigms for engineering atom-light interactions and provide a potentially scalable route for quantum sensing, metrology, and quantum information processing. However, it remains a challenging task to efficiently trap a large ensemble of cold atoms on an integrated nanophotonic circuit. Here, we demonstrate direct loading of an ensemble of up to 70 atoms into an optical microtrap on a nanophotonic microring circuit. Efficient trap loading is achieved by employing degenerate Raman-sideband cooling in the microtrap, where a built-in spin-motion coupling arises directly from the vector light shift of the evanescent-field potential on a microring. Atoms are cooled into the trap via optical pumping with a single free space beam. We have achieved a trap lifetime approaching 700 ms under continuous cooling. We show that the trapped atoms display large cooperative coupling and superradiant decay into a whispering-gallery mode of the microring resonator, holding promise for explorations of new collective effects. Our technique can be extended to trapping a large ensemble of cold atoms on nanophotonic circuits for various quantum applications.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141561506","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 : 2024-07-09DOI: 10.1103/physrevx.14.031003
Pei-Kai Tsai, Yue Wu, Shruti Puri
An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomenon of fragile temporal boundaries that arises during the standard logical state-preparation and measurement protocols. To address this challenge we propose a new logical state-preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard protocol in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement.
{"title":"Mitigating Temporal Fragility in the XY Surface Code","authors":"Pei-Kai Tsai, Yue Wu, Shruti Puri","doi":"10.1103/physrevx.14.031003","DOIUrl":"https://doi.org/10.1103/physrevx.14.031003","url":null,"abstract":"An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomenon of fragile temporal boundaries that arises during the standard logical state-preparation and measurement protocols. To address this challenge we propose a new logical state-preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>O</mi><mo stretchy=\"false\">(</mo><msqrt><mi>n</mi></msqrt><mo stretchy=\"false\">)</mo></math> high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard protocol in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141561509","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 : 2024-07-08DOI: 10.1103/physrevx.14.031002
Yicheng Bao, Scarlett S. Yu, Jiaqi You, Loïc Anderegg, Eunmi Chae, Wolfgang Ketterle, Kang-Kuen Ni, John M. Doyle
Ultracold polar molecules are promising for quantum information processing and searches for physics beyond the standard model. Laser cooling to ultracold temperatures is an established technique for trapped diatomic and triatomic molecules. Further cooling of the molecules to near the motional ground state is crucial for reducing various dephasings in quantum and precision applications. In this work, we demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their motional ground state, with average motional occupation quantum numbers of , (radial directions), and (axial direction), and a 3-D motional-ground-state probability of of the molecules that survive the RSC. This process paves the way to increase molecular coherence times in optical tweezers for robust quantum computation and simulation applications.
{"title":"Raman Sideband Cooling of Molecules in an Optical Tweezer Array to the 3D Motional Ground State","authors":"Yicheng Bao, Scarlett S. Yu, Jiaqi You, Loïc Anderegg, Eunmi Chae, Wolfgang Ketterle, Kang-Kuen Ni, John M. Doyle","doi":"10.1103/physrevx.14.031002","DOIUrl":"https://doi.org/10.1103/physrevx.14.031002","url":null,"abstract":"Ultracold polar molecules are promising for quantum information processing and searches for physics beyond the standard model. Laser cooling to ultracold temperatures is an established technique for trapped diatomic and triatomic molecules. Further cooling of the molecules to near the motional ground state is crucial for reducing various dephasings in quantum and precision applications. In this work, we demonstrate Raman sideband cooling (RSC) of CaF molecules in optical tweezers to near their motional ground state, with average motional occupation quantum numbers of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mover accent=\"true\"><mi>n</mi><mo stretchy=\"false\">¯</mo></mover><mi>x</mi></msub><mo>=</mo><mn>0.16</mn><mo stretchy=\"false\">(</mo><mn>12</mn><mo stretchy=\"false\">)</mo></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mover accent=\"true\"><mi>n</mi><mo stretchy=\"false\">¯</mo></mover><mi>y</mi></msub><mo>=</mo><mn>0.17</mn><mo stretchy=\"false\">(</mo><mn>17</mn><mo stretchy=\"false\">)</mo></math> (radial directions), and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mover accent=\"true\"><mi>n</mi><mo stretchy=\"false\">¯</mo></mover><mi>z</mi></msub><mo>=</mo><mn>0.22</mn><mo stretchy=\"false\">(</mo><mn>16</mn><mo stretchy=\"false\">)</mo></math> (axial direction), and a 3-D motional-ground-state probability of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>54</mn><mo>±</mo><mn>18</mn><mo>%</mo></math> of the molecules that survive the RSC. This process paves the way to increase molecular coherence times in optical tweezers for robust quantum computation and simulation applications.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141561232","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 : 2024-07-01DOI: 10.1103/physrevx.14.031001
Francesco Cagnetta, Leonardo Petrini, Umberto M. Tomasini, Alessandro Favero, Matthieu Wyart
Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representations. However, how many training examples are required to learn such representations remains unknown. To quantitatively study this question, we introduce the random hierarchy model: a family of synthetic tasks inspired by the hierarchical structure of language and images. The model is a classification task where each class corresponds to a group of high-level features, chosen among several equivalent groups associated with the same class. In turn, each feature corresponds to a group of subfeatures chosen among several equivalent groups and so on, following a hierarchy of composition rules. We find that deep networks learn the task by developing internal representations invariant to exchanging equivalent groups. Moreover, the number of data required corresponds to the point where correlations between low-level features and classes become detectable. Overall, our results indicate how deep networks overcome the curse of dimensionality by building invariant representations and provide an estimate of the number of data required to learn a hierarchical task.
{"title":"How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model","authors":"Francesco Cagnetta, Leonardo Petrini, Umberto M. Tomasini, Alessandro Favero, Matthieu Wyart","doi":"10.1103/physrevx.14.031001","DOIUrl":"https://doi.org/10.1103/physrevx.14.031001","url":null,"abstract":"Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representations. However, how many training examples are required to learn such representations remains unknown. To quantitatively study this question, we introduce the random hierarchy model: a family of synthetic tasks inspired by the hierarchical structure of language and images. The model is a classification task where each class corresponds to a group of high-level features, chosen among several equivalent groups associated with the same class. In turn, each feature corresponds to a group of subfeatures chosen among several equivalent groups and so on, following a hierarchy of composition rules. We find that deep networks learn the task by developing internal representations invariant to exchanging equivalent groups. Moreover, the number of data required corresponds to the point where correlations between low-level features and classes become detectable. Overall, our results indicate how deep networks overcome the curse of dimensionality by building invariant representations and provide an estimate of the number of data required to learn a hierarchical task.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489148","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 : 2024-06-27DOI: 10.1103/physrevx.14.021053
Weicheng Ye, Liujun Zou
We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify chiral states and non-Abelian states enriched by a or symmetry and topological orders and topological orders enriched by a , , , or
{"title":"Classification of Symmetry-Enriched Topological Quantum Spin Liquids","authors":"Weicheng Ye, Liujun Zou","doi":"10.1103/physrevx.14.021053","DOIUrl":"https://doi.org/10.1103/physrevx.14.021053","url":null,"abstract":"We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><msub><mo stretchy=\"false\">)</mo><mrow><mn>2</mn><mi>N</mi></mrow></msub></math> chiral states and non-Abelian <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mrow><mi>Ising</mi></mrow><mrow><mo stretchy=\"false\">(</mo><mi>ν</mi><mo stretchy=\"false\">)</mo></mrow></msup></mrow></math> states enriched by a <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>6</mn><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math> or <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>4</mn><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math> symmetry and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"double-struck\">Z</mi><mi>N</mi></msub></math> topological orders and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><msub><mo stretchy=\"false\">)</mo><mrow><mn>2</mn><mi>N</mi></mrow></msub><mo>×</mo><mi mathvariant=\"normal\">U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><msub><mo stretchy=\"false\">)</mo><mrow><mo>−</mo><mn>2</mn><mi>N</mi></mrow></msub></math> topological orders enriched by a <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>6</mn><mi>m</mi><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msubsup><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>4</mn><mi>m</mi><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msubsup><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>6</mn><mi>m</mi><mo>×</mo><msubsup><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, or <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>4</mn><mi>m</mi>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141462640","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 : 2024-06-26DOI: 10.1103/physrevx.14.021052
Carl Philipp Zelle, Romain Daviet, Achim Rosch, Sebastian Diehl
In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for , and a generalization for arbitrary , which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium.
{"title":"Universal Phenomenology at Critical Exceptional Points of Nonequilibrium O(N) Models","authors":"Carl Philipp Zelle, Romain Daviet, Achim Rosch, Sebastian Diehl","doi":"10.1103/physrevx.14.021052","DOIUrl":"https://doi.org/10.1103/physrevx.14.021052","url":null,"abstract":"In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">O</mi><mo stretchy=\"false\">(</mo><mi>N</mi><mo stretchy=\"false\">)</mo></mrow></math> field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mi>N</mi><mo>−</mo><mn>3</mn></math> Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi><mo><</mo><mn>4</mn></math> they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi><mo>=</mo><mn>2</mn></math>, and a generalization for arbitrary <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math>, which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi><mi>y</mi></math> magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141453027","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 : 2024-06-21DOI: 10.1103/physrevx.14.021050
Sebastiano Bontorin, Giulia Cencetti, Riccardo Gallotti, Bruno Lepri, Manlio De Domenico
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral branches, which can appear both in natural and manmade systems, such as subway and railway networks. In this study, we investigate the conditions for the emergence of these nontrivial topological structures in the context of human transportation in cities. We propose a simple model for spatial networks generation, where a network lattice acts as a planar substrate and edge speeds define an effective temporal distance which we aim to optimize and quantifies the efficiency in exploring the urban space. Complex network topologies can be recovered from the optimization of edges’ speeds and we study how the interplay between a flow probability between two nodes in space and the associated travel cost influences the resulting optimal network. In the perspective of urban transportation we simulate these flows by means of human mobility models to obtain origin-destination matrices. We find that when using simple lattices, the obtained optimal topologies transition from treelike structures to more regular networks, depending on the spatial range of flows. Remarkably, we find that branches paired to large loops structures appear as optimal structures when the network is optimized for an interplay between heterogeneous mobility patterns of small range travels and longer-range ones typical of commuting. Moreover, when congestion dynamics in traffic routing is considered, we study the emergence of additional edges from the tree structure to mitigate temporal delays. Finally, we show that our framework is able to recover the statistical spatial properties of the Greater London area subway network.
{"title":"Emergence of Complex Network Topologies from Flow-Weighted Optimization of Network Efficiency","authors":"Sebastiano Bontorin, Giulia Cencetti, Riccardo Gallotti, Bruno Lepri, Manlio De Domenico","doi":"10.1103/physrevx.14.021050","DOIUrl":"https://doi.org/10.1103/physrevx.14.021050","url":null,"abstract":"Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral branches, which can appear both in natural and manmade systems, such as subway and railway networks. In this study, we investigate the conditions for the emergence of these nontrivial topological structures in the context of human transportation in cities. We propose a simple model for spatial networks generation, where a network lattice acts as a planar substrate and edge speeds define an effective temporal distance which we aim to optimize and quantifies the efficiency in exploring the urban space. Complex network topologies can be recovered from the optimization of edges’ speeds and we study how the interplay between a flow probability between two nodes in space and the associated travel cost influences the resulting optimal network. In the perspective of urban transportation we simulate these flows by means of human mobility models to obtain origin-destination matrices. We find that when using simple lattices, the obtained optimal topologies transition from treelike structures to more regular networks, depending on the spatial range of flows. Remarkably, we find that branches paired to large loops structures appear as optimal structures when the network is optimized for an interplay between heterogeneous mobility patterns of small range travels and longer-range ones typical of commuting. Moreover, when congestion dynamics in traffic routing is considered, we study the emergence of additional edges from the tree structure to mitigate temporal delays. Finally, we show that our framework is able to recover the statistical spatial properties of the Greater London area subway network.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":12.5,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141435802","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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