Pub Date : 2020-11-10DOI: 10.1103/PhysRevB.103.205107
Chen-yu Liu, Da-wei Wang
The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as the system size increases. A few numerical methods have been developed for some specific systems, but may not be applicable in others. Here we propose a general numerical method, Random Sampling Neural Networks (RSNN), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach. Several exactly solvable 1D models, including Ising model with transverse field, Fermi-Hubbard model, and spin-$1/2$ $XXZ$ model, are used to test the applicability of RSNN. Pretty high accuracy of energy spectrum, magnetization and critical exponents etc. can be obtained within the strongly correlated regime or near the quantum phase transition point, even the corresponding RSNN models are trained in the weakly interacting regime. The required computation time scales linearly to the system size. Our results demonstrate that it is possible to combine the existing numerical methods for the training process and RSNN to explore quantum many-body problems in a much wider parameter regime, even for strongly correlated systems.
{"title":"Random sampling neural network for quantum many-body problems","authors":"Chen-yu Liu, Da-wei Wang","doi":"10.1103/PhysRevB.103.205107","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.205107","url":null,"abstract":"The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as the system size increases. A few numerical methods have been developed for some specific systems, but may not be applicable in others. Here we propose a general numerical method, Random Sampling Neural Networks (RSNN), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach. Several exactly solvable 1D models, including Ising model with transverse field, Fermi-Hubbard model, and spin-$1/2$ $XXZ$ model, are used to test the applicability of RSNN. Pretty high accuracy of energy spectrum, magnetization and critical exponents etc. can be obtained within the strongly correlated regime or near the quantum phase transition point, even the corresponding RSNN models are trained in the weakly interacting regime. The required computation time scales linearly to the system size. Our results demonstrate that it is possible to combine the existing numerical methods for the training process and RSNN to explore quantum many-body problems in a much wider parameter regime, even for strongly correlated systems.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72875477","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}
G. Baxter, R. da Costa, S. N. Dorogovtsev, J. Mendes
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. The authors fully describe the critical phenomena of this process. In two layers with finite second moments of the degree distributions the authors observe an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers the authors find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+1/(M-1)$ for $M$ layers.
{"title":"Weak Multiplex Percolation","authors":"G. Baxter, R. da Costa, S. N. Dorogovtsev, J. Mendes","doi":"10.1017/9781108865777","DOIUrl":"https://doi.org/10.1017/9781108865777","url":null,"abstract":"In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. The authors fully describe the critical phenomena of this process. In two layers with finite second moments of the degree distributions the authors observe an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers the authors find a discontinuous hybrid transition which persists even in highly heterogeneous degree distributions, becoming continuous only when the powerlaw exponent reaches $1+1/(M-1)$ for $M$ layers.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"115 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79019235","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 : 2020-11-02DOI: 10.1103/PHYSREVMATERIALS.5.015602
Zheng Yu, Qitong Liu, I. Szlufarska, Bu Wang
The structure-thermodynamic stability relationship in vitreous silica is investigated using machine learning and a library of 24,157 inherent structures generated from melt-quenching and replica exchange molecular dynamics simulations. We find the thermodynamic stability, i.e., enthalpy of the inherent structure ($e_{mathrm{IS}}$), can be accurately predicted by both linear and nonlinear machine learning models from numeric structural descriptors commonly used to characterize disordered structures. We find short-range features become less indicative of thermodynamic stability below the fragile-to-strong transition. On the other hand, medium-range features, especially those between 2.8-~6 $unicode{x212B}$;, show consistent correlations with $e_{mathrm{IS}}$ across the liquid and glass regions, and are found to be the most critical to stability prediction among features from different length scales. Based on the machine learning models, a set of five structural features that are the most predictive of the silica glass stability is identified.
{"title":"Structural signatures for thermodynamic stability in vitreous silica: Insight from machine learning and molecular dynamics simulations","authors":"Zheng Yu, Qitong Liu, I. Szlufarska, Bu Wang","doi":"10.1103/PHYSREVMATERIALS.5.015602","DOIUrl":"https://doi.org/10.1103/PHYSREVMATERIALS.5.015602","url":null,"abstract":"The structure-thermodynamic stability relationship in vitreous silica is investigated using machine learning and a library of 24,157 inherent structures generated from melt-quenching and replica exchange molecular dynamics simulations. We find the thermodynamic stability, i.e., enthalpy of the inherent structure ($e_{mathrm{IS}}$), can be accurately predicted by both linear and nonlinear machine learning models from numeric structural descriptors commonly used to characterize disordered structures. We find short-range features become less indicative of thermodynamic stability below the fragile-to-strong transition. On the other hand, medium-range features, especially those between 2.8-~6 $unicode{x212B}$;, show consistent correlations with $e_{mathrm{IS}}$ across the liquid and glass regions, and are found to be the most critical to stability prediction among features from different length scales. Based on the machine learning models, a set of five structural features that are the most predictive of the silica glass stability is identified.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79975933","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 : 2020-10-21DOI: 10.21468/SCIPOSTPHYSCORE.4.2.008
Corrado Rainone, Eran Bouchbinder, E. Lerner, P. Urbani, F. Zamponi
Structural glasses feature quasilocalized excitations whose frequencies $omega$ follow a universal density of states ${cal D}(omega)!sim!omega^4$. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $kappa_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${cal D}(omega)!=!A_{rm g},omega^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then -- using scaling theory and numerical simulations -- we provide a complete understanding of the non-universal prefactor $A_{rm g}(h,J,kappa_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{rm g}(h,J,kappa_0)$ is a nonmonotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(kappa_0 h^{2/3}!/J^2)$ in the weak interactions (small $J$) regime -- reminiscent of recent observations in computer glasses -- and predominantly decaying as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.
{"title":"Mean-field model of interacting quasilocalized excitations in glasses","authors":"Corrado Rainone, Eran Bouchbinder, E. Lerner, P. Urbani, F. Zamponi","doi":"10.21468/SCIPOSTPHYSCORE.4.2.008","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYSCORE.4.2.008","url":null,"abstract":"Structural glasses feature quasilocalized excitations whose frequencies $omega$ follow a universal density of states ${cal D}(omega)!sim!omega^4$. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $kappa_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${cal D}(omega)!=!A_{rm g},omega^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then -- using scaling theory and numerical simulations -- we provide a complete understanding of the non-universal prefactor $A_{rm g}(h,J,kappa_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{rm g}(h,J,kappa_0)$ is a nonmonotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(kappa_0 h^{2/3}!/J^2)$ in the weak interactions (small $J$) regime -- reminiscent of recent observations in computer glasses -- and predominantly decaying as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"116 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86210670","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 : 2020-10-17DOI: 10.21468/SciPostPhys.10.5.107
'Angel L. Corps, R. Molina, A. Relaño
Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a signature that unambiguously identifies a possible finite-size precursor of a critical point, and distinguishes between two different stages of the transition. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered $J_1$-$J_2$ model. Both the particular value of this maximum and the disorder strength at which it is reached increase with the system size, as expected for a typical finite-size scaling. We completely characterize the short and long-range spectral statistics of the model and find that their behavior perfectly correlates with the properties of the diagonal fluctuations. For lower values of the disorder, we find a chaotic region in which the Thouless energy diminishes up to the transition point, at which it becomes equal to the Heisenberg energy. For larger values of disorder, spectral statistics are very well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior.
{"title":"Signatures of a critical point in the many-body localization transition","authors":"'Angel L. Corps, R. Molina, A. Relaño","doi":"10.21468/SciPostPhys.10.5.107","DOIUrl":"https://doi.org/10.21468/SciPostPhys.10.5.107","url":null,"abstract":"Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition region between them is not fully understood yet. We propose here a signature that unambiguously identifies a possible finite-size precursor of a critical point, and distinguishes between two different stages of the transition. The kurtosis excess of the diagonal fluctuations of the full one-dimensional momentum distribution from its microcanonical average is maximum at this singular point in the paradigmatic disordered $J_1$-$J_2$ model. Both the particular value of this maximum and the disorder strength at which it is reached increase with the system size, as expected for a typical finite-size scaling. We completely characterize the short and long-range spectral statistics of the model and find that their behavior perfectly correlates with the properties of the diagonal fluctuations. For lower values of the disorder, we find a chaotic region in which the Thouless energy diminishes up to the transition point, at which it becomes equal to the Heisenberg energy. For larger values of disorder, spectral statistics are very well described by a generalized semi-Poissonian model, eventually leading to the integrable Poissonian behavior.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88203197","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 : 2020-10-13DOI: 10.1103/physrevb.102.195132
Yang Zhao, Dingyi Feng, Yongbo Hu, Shutong Guo, J. Sirker
We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $simlnln t$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.
{"title":"Entanglement dynamics in the three-dimensional Anderson model","authors":"Yang Zhao, Dingyi Feng, Yongbo Hu, Shutong Guo, J. Sirker","doi":"10.1103/physrevb.102.195132","DOIUrl":"https://doi.org/10.1103/physrevb.102.195132","url":null,"abstract":"We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $simlnln t$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85982708","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 : 2020-10-12DOI: 10.1103/PhysRevResearch.3.023230
Jui-Hui Chung, Y. Kao
The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters. However, finding the optimal RG transformation remains difficult due to the many possible choices of the weight factors in the RG procedure. Here we show, by identifying the conditional distribution in the restricted Boltzmann machine (RBM) and the weight factor distribution in the RG procedure, an optimal real-space RG transformation can be learned without prior knowledge of the physical system. This neural Monte Carlo RG algorithm allows for direct computation of the RG flow and critical exponents. This scheme naturally generates a transformation that maximizes the real-space mutual information between the coarse-grained region and the environment. Our results establish a solid connection between the RG transformation in physics and the deep architecture in machine learning, paving the way to further interdisciplinary research.
{"title":"Neural Monte Carlo renormalization group","authors":"Jui-Hui Chung, Y. Kao","doi":"10.1103/PhysRevResearch.3.023230","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.3.023230","url":null,"abstract":"The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters. However, finding the optimal RG transformation remains difficult due to the many possible choices of the weight factors in the RG procedure. Here we show, by identifying the conditional distribution in the restricted Boltzmann machine (RBM) and the weight factor distribution in the RG procedure, an optimal real-space RG transformation can be learned without prior knowledge of the physical system. This neural Monte Carlo RG algorithm allows for direct computation of the RG flow and critical exponents. This scheme naturally generates a transformation that maximizes the real-space mutual information between the coarse-grained region and the environment. Our results establish a solid connection between the RG transformation in physics and the deep architecture in machine learning, paving the way to further interdisciplinary research.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87697725","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 : 2020-10-07DOI: 10.1103/PhysRevB.103.214205
Claudia Artiaco, F. Balducci, A. Scardicchio
We study the dynamics and the spread of entanglement of two-level systems (TLSs) in amorphous solids at low temperatures (around 1K). By considering the coupling to phonons within the framework of the Lindblad equation, we show that the wide distribution of disorder leads to all sorts slow dynamics for the TLSs, that can be interpreted within the theory of many-body localization (MBL). In particular, we show that the power-law decay of the concurrence, which is typical of MBL isolated systems, survives the coupling to phonons in a wide region of parameter space. We discuss the relevance and implications for experiments.
{"title":"Signatures of many-body localization in the dynamics of two-level systems in glasses","authors":"Claudia Artiaco, F. Balducci, A. Scardicchio","doi":"10.1103/PhysRevB.103.214205","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.214205","url":null,"abstract":"We study the dynamics and the spread of entanglement of two-level systems (TLSs) in amorphous solids at low temperatures (around 1K). By considering the coupling to phonons within the framework of the Lindblad equation, we show that the wide distribution of disorder leads to all sorts slow dynamics for the TLSs, that can be interpreted within the theory of many-body localization (MBL). In particular, we show that the power-law decay of the concurrence, which is typical of MBL isolated systems, survives the coupling to phonons in a wide region of parameter space. We discuss the relevance and implications for experiments.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79009640","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}
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous systems. We summarize the properties of topological states and discuss how disposing of translational invariance has motivated the surge of new tools to characterize topological states in amorphous systems, both theoretically and experimentally. The ubiquity of amorphous systems combined with the robustness of topology has the potential to bring new fundamental understanding in our classification of phases of matter, and inspire new technological developments.
{"title":"Low-Temperature Thermal and Vibrational Properties of Disordered Solids","authors":"A. Grushin","doi":"10.1142/q0371","DOIUrl":"https://doi.org/10.1142/q0371","url":null,"abstract":"Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous systems. We summarize the properties of topological states and discuss how disposing of translational invariance has motivated the surge of new tools to characterize topological states in amorphous systems, both theoretically and experimentally. The ubiquity of amorphous systems combined with the robustness of topology has the potential to bring new fundamental understanding in our classification of phases of matter, and inspire new technological developments.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89213149","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 : 2020-09-23DOI: 10.1103/physrevb.102.214201
Y. Mohdeb, J. Vahedi, N. Moure, A. Roshani, Hyunyong Lee, R. Bhatt, S. Kettemann, S. Haas
We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $alpha$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $alpha > 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $alpha$, corresponding to a critical behavior with an effective central charge $c = {rm ln} 2$, independent of $alpha$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $alpha$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $alpha =2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.
{"title":"Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions","authors":"Y. Mohdeb, J. Vahedi, N. Moure, A. Roshani, Hyunyong Lee, R. Bhatt, S. Kettemann, S. Haas","doi":"10.1103/physrevb.102.214201","DOIUrl":"https://doi.org/10.1103/physrevb.102.214201","url":null,"abstract":"We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $alpha$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $alpha > 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $alpha$, corresponding to a critical behavior with an effective central charge $c = {rm ln} 2$, independent of $alpha$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $alpha$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $alpha =2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76622593","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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