Pub Date : 2017-09-08DOI: 10.1103/PhysRevB.97.094207
W. Rao, Zhenyu Li, Q. Zhu, Mingxing Luo, Xin Wan
Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from non-ergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.
{"title":"Identifying Product Order with Restricted Boltzmann Machines","authors":"W. Rao, Zhenyu Li, Q. Zhu, Mingxing Luo, Xin Wan","doi":"10.1103/PhysRevB.97.094207","DOIUrl":"https://doi.org/10.1103/PhysRevB.97.094207","url":null,"abstract":"Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from non-ergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85804558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Short-range order (SRO) in disordered alloys is typically interpreted as competition between chemical effect of negative (or positive) energy gain by mixing constituent elements and geometric effects comes from difference in effective atomic radius. Although we have a number of theoretical approaches to quantitatively estimate SRO at given temperatures, it is still unclear to systematically understand trends in SRO for binary alloys in terms of geometric character, e.g., effective atomic radius for constituents. Since chemical effect plays significant role on SRO, it has been believed that purely geometric character cannot quantitatively explain the SRO trends. Despite these considerations, based on the density functional theory (DFT) calculations on fcc-based 28 equiatomic binary alloys, we find that while convensional Goldschmidt or DFT-based atomic radius for constituents have no significant correlation with SRO, atomic radius for specially selected structure, constructed purely from information about underlying lattice, can successfully capture the magnitude of SRO. These facts strongly indicate that purely geometric information of the system plays central role to determine characteristic disordered structure.
{"title":"Short-Range-Order for fcc-based binary alloys Revisited from Microscopic Geometry","authors":"Koretaka Yuge","doi":"10.7566/JPSJ.87.044804","DOIUrl":"https://doi.org/10.7566/JPSJ.87.044804","url":null,"abstract":"Short-range order (SRO) in disordered alloys is typically interpreted as competition between chemical effect of negative (or positive) energy gain by mixing constituent elements and geometric effects comes from difference in effective atomic radius. Although we have a number of theoretical approaches to quantitatively estimate SRO at given temperatures, it is still unclear to systematically understand trends in SRO for binary alloys in terms of geometric character, e.g., effective atomic radius for constituents. Since chemical effect plays significant role on SRO, it has been believed that purely geometric character cannot quantitatively explain the SRO trends. Despite these considerations, based on the density functional theory (DFT) calculations on fcc-based 28 equiatomic binary alloys, we find that while convensional Goldschmidt or DFT-based atomic radius for constituents have no significant correlation with SRO, atomic radius for specially selected structure, constructed purely from information about underlying lattice, can successfully capture the magnitude of SRO. These facts strongly indicate that purely geometric information of the system plays central role to determine characteristic disordered structure.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84484467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-15DOI: 10.21468/SciPostPhys.4.5.025
S. Roy, Ivan M Khaymovich, Arnab Das, R. Moessner
Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band of multifractal wavefunctions in a periodically driven chain of non-interacting particles subject to spatially quasiperiodic disorder. Remarkably, this multifractality is robust in that it does not require any fine-tuning of the model parameters, which sets it apart from the known multifractality of $critical$ wavefunctions. The multifractality arises as the periodic drive hybridises the localised and delocalised sectors of the undriven spectrum. We account for this phenomenon in a simple random matrix based theory. Finally, we discuss dynamical signatures of the multifractal states, which should betray their presence in cold atom experiments. Such a simple yet robust realisation of multifractality could advance this so far elusive phenomenon towards applications, such as the proposed disorder-induced enhancement of a superfluid transition.
{"title":"Multifractality without fine-tuning in a Floquet quasiperiodic chain.","authors":"S. Roy, Ivan M Khaymovich, Arnab Das, R. Moessner","doi":"10.21468/SciPostPhys.4.5.025","DOIUrl":"https://doi.org/10.21468/SciPostPhys.4.5.025","url":null,"abstract":"Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band of multifractal wavefunctions in a periodically driven chain of non-interacting particles subject to spatially quasiperiodic disorder. Remarkably, this multifractality is robust in that it does not require any fine-tuning of the model parameters, which sets it apart from the known multifractality of $critical$ wavefunctions. The multifractality arises as the periodic drive hybridises the localised and delocalised sectors of the undriven spectrum. We account for this phenomenon in a simple random matrix based theory. Finally, we discuss dynamical signatures of the multifractal states, which should betray their presence in cold atom experiments. Such a simple yet robust realisation of multifractality could advance this so far elusive phenomenon towards applications, such as the proposed disorder-induced enhancement of a superfluid transition.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84941547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-05-02DOI: 10.1103/PhysRevB.97.014414
Cosimo Lupo, F. Ricci-Tersenghi
Vector spin glasses are known to show two different kinds of phase transitions in presence of an external field: the so-called de Almeida-Thouless and Gabay-Toulouse lines. In the literature both critical lines have been computed only for fully connected models, which are known to show some unphysical behaviors (e. g. the divergence of these critical lines in the zero-temperature limit). Here we compute analytically these critical lines for XY spin glasses on random regular graphs. We discuss the different nature of these phase transitions and the dependence of the critical behavior on the field distribution. We also study the crossover between the two different critical behaviors.
{"title":"Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for the spin glass XY model in a field on sparse random graphs","authors":"Cosimo Lupo, F. Ricci-Tersenghi","doi":"10.1103/PhysRevB.97.014414","DOIUrl":"https://doi.org/10.1103/PhysRevB.97.014414","url":null,"abstract":"Vector spin glasses are known to show two different kinds of phase transitions in presence of an external field: the so-called de Almeida-Thouless and Gabay-Toulouse lines. In the literature both critical lines have been computed only for fully connected models, which are known to show some unphysical behaviors (e. g. the divergence of these critical lines in the zero-temperature limit). Here we compute analytically these critical lines for XY spin glasses on random regular graphs. We discuss the different nature of these phase transitions and the dependence of the critical behavior on the field distribution. We also study the crossover between the two different critical behaviors.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73729598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-04-15DOI: 10.21468/SciPostPhys.4.4.020
G. Biroli, P. Urbani
We study Harmonic Soft Spheres as a model of thermal structural glasses in the limit of infinite dimensions. We show that cooling, compressing and shearing a glass lead to a Gardner transition and, hence, to a marginally stable amorphous solid as found for Hard Spheres systems. A general outcome of our results is that a reduced stability of the glass favors the appearance of the Gardner transition. Therefore using strong perturbations, e.g. shear and compression, on standard glasses or using weak perturbations on weakly stable glasses, e.g. the ones prepared close to the jamming point, are the generic ways to induce a Gardner transition. The formalism that we discuss allows to study general perturbations, including strain deformations that are important to study soft glassy rheology at the mean field level.
{"title":"Liu-Nagel phase diagrams in infinite dimension","authors":"G. Biroli, P. Urbani","doi":"10.21468/SciPostPhys.4.4.020","DOIUrl":"https://doi.org/10.21468/SciPostPhys.4.4.020","url":null,"abstract":"We study Harmonic Soft Spheres as a model of thermal structural glasses in the limit of infinite dimensions. We show that cooling, compressing and shearing a glass lead to a Gardner transition and, hence, to a marginally stable amorphous solid as found for Hard Spheres systems. A general outcome of our results is that a reduced stability of the glass favors the appearance of the Gardner transition. Therefore using strong perturbations, e.g. shear and compression, on standard glasses or using weak perturbations on weakly stable glasses, e.g. the ones prepared close to the jamming point, are the generic ways to induce a Gardner transition. The formalism that we discuss allows to study general perturbations, including strain deformations that are important to study soft glassy rheology at the mean field level.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90528175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-04-03DOI: 10.1103/PhysRevB.97.201105
Johnnie Gray, S. Bose, A. Bayat
Many-body localization has become an important phenomenon for illuminating a potential rift between non-equilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent $nu ge 2$ in one dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find $nu sim 1$. We introduce the Schmidt gap, new in this context, which scales near the transition with a exponent $nu > 2$ compatible with the analytical bound. We attribute this to an insensitivity to certain finite size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.
多体局域化已成为揭示非平衡量子系统与统计力学之间潜在裂缝的重要现象。然而，在显示多体局部化的模型中，遍历阶段和局部阶段之间的过渡的性质尚未得到很好的理解。假设这是一个连续的过渡，分析结果表明，在一维系统中，长度尺度应该以一个临界指数$nu ge 2$发散。有趣的是，这与所有精确的数值研究发现$nu sim 1$形成鲜明对比。我们引入Schmidt间隙，在这种情况下是新的，它在转换附近缩放，其指数$nu > 2$与解析界兼容。我们将此归因于对某些有限尺寸波动的不敏感，这些波动在精确数值方法可达到的尺寸下的其他数量中仍然很重要。此外，我们发现在使用不相交块之间的对数负性计算的纠缠长度中，发散长度尺度的物理表现是明显的。
{"title":"Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling","authors":"Johnnie Gray, S. Bose, A. Bayat","doi":"10.1103/PhysRevB.97.201105","DOIUrl":"https://doi.org/10.1103/PhysRevB.97.201105","url":null,"abstract":"Many-body localization has become an important phenomenon for illuminating a potential rift between non-equilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent $nu ge 2$ in one dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find $nu sim 1$. We introduce the Schmidt gap, new in this context, which scales near the transition with a exponent $nu > 2$ compatible with the analytical bound. We attribute this to an insensitivity to certain finite size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82513710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-03-10DOI: 10.1103/PhysRevB.97.100301
Soonwon Choi, D. Abanin, M. Lukin
We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe non-equilibrium phases of matter for a long time, limited only by coupling to external environment.
{"title":"Dynamically induced many-body localization","authors":"Soonwon Choi, D. Abanin, M. Lukin","doi":"10.1103/PhysRevB.97.100301","DOIUrl":"https://doi.org/10.1103/PhysRevB.97.100301","url":null,"abstract":"We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe non-equilibrium phases of matter for a long time, limited only by coupling to external environment.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79692028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-02-10DOI: 10.1103/physrevx.7.031061
A. Chandran, C. Laumann
Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic and quasiperiodically alternating ground state phases with extended, localized and critically delocalized low energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-Andr'e duality which we develop. The quasiperiodic Ising glass may be realized in near term quantum optical experiments.
{"title":"Localization and symmetry breaking in the quantum quasiperiodic Ising glass","authors":"A. Chandran, C. Laumann","doi":"10.1103/physrevx.7.031061","DOIUrl":"https://doi.org/10.1103/physrevx.7.031061","url":null,"abstract":"Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a emph{quasiperiodic Ising glass} stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic and quasiperiodically alternating ground state phases with extended, localized and critically delocalized low energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-Andr'e duality which we develop. The quasiperiodic Ising glass may be realized in near term quantum optical experiments.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89531334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Our recent study elucidate that information of density of states in configuration space (CDOS) for non-interacting system, characterized by spatial constraint on the system, plays essential role to determine thermodynamically equilibrium properties for interacting systems. Particularly for disordered states, variance of CDOS along all possible coordinations plays significant role. Despite this fact, even for binary system of crystalline solids, analytic expression for variance of CDOS as a function of composition has not been clarified so far. Here we successfully derive variance of CDOS as a function of composition for pair correlations, whose validity is demonstrated by comparing the results with uniform sampling of CDOS on real lattices. The present result certainly advances determining special microscopic state to characterize Helmholtz free energy in classical systems, whose structure is difficult to determine by numerical simulation.
{"title":"Analytic Determination of Variance for Configurational Density of States in Crystalline Solids","authors":"Tetyuya Taikei, Kazuhito Takeuchi, Koretaka Yuge","doi":"10.14723/tmrsj.42.81","DOIUrl":"https://doi.org/10.14723/tmrsj.42.81","url":null,"abstract":"Our recent study elucidate that information of density of states in configuration space (CDOS) for non-interacting system, characterized by spatial constraint on the system, plays essential role to determine thermodynamically equilibrium properties for interacting systems. Particularly for disordered states, variance of CDOS along all possible coordinations plays significant role. Despite this fact, even for binary system of crystalline solids, analytic expression for variance of CDOS as a function of composition has not been clarified so far. Here we successfully derive variance of CDOS as a function of composition for pair correlations, whose validity is demonstrated by comparing the results with uniform sampling of CDOS on real lattices. The present result certainly advances determining special microscopic state to characterize Helmholtz free energy in classical systems, whose structure is difficult to determine by numerical simulation.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88591712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-01-17DOI: 10.1103/PhysRevX.7.021021
D. Deng, Xiaopeng Li, Xiaopeng Li, S. Sarma
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states is recently becoming highly desirable in the applications of machine learning techniques to quantum many-body physics. Here, we study the quantum entanglement properties of neural-network states, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing efficiently quantum states with massive entanglement. We further examine generic RBM states with random weight parameters. We find that their averaged entanglement entropy obeys volume-law scaling and meantime strongly deviates from the Page-entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states, which paves a novel way to bridge computer science based machine learning techniques to outstanding quantum condensed matter physics problems.
{"title":"Quantum Entanglement in Neural Network States","authors":"D. Deng, Xiaopeng Li, Xiaopeng Li, S. Sarma","doi":"10.1103/PhysRevX.7.021021","DOIUrl":"https://doi.org/10.1103/PhysRevX.7.021021","url":null,"abstract":"Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial neural-network states is recently becoming highly desirable in the applications of machine learning techniques to quantum many-body physics. Here, we study the quantum entanglement properties of neural-network states, with a focus on the restricted-Boltzmann-machine (RBM) architecture. We prove that the entanglement of all short-range RBM states satisfies an area law for arbitrary dimensions and bipartition geometry. For long-range RBM states we show by using an exact construction that such states could exhibit volume-law entanglement, implying a notable capability of RBM in representing efficiently quantum states with massive entanglement. We further examine generic RBM states with random weight parameters. We find that their averaged entanglement entropy obeys volume-law scaling and meantime strongly deviates from the Page-entropy of the completely random pure states. We show that their entanglement spectrum has no universal part associated with random matrix theory and bears a Poisson-type level statistics. Using reinforcement learning, we demonstrate that RBM is capable of finding the ground state (with power-law entanglement) of a model Hamiltonian with long-range interaction. In addition, we show, through a concrete example of the one-dimensional symmetry-protected topological cluster states, that the RBM representation may also be used as a tool to analytically compute the entanglement spectrum. Our results uncover the unparalleled power of artificial neural networks in representing quantum many-body states, which paves a novel way to bridge computer science based machine learning techniques to outstanding quantum condensed matter physics problems.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87656078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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