arXiv: Disordered Systems and Neural Networks最新文献_第2页

Random sampling neural network for quantum many-body problems 量子多体问题的随机抽样神经网络

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-11-10 DOI: 10.1103/PhysRevB.103.205107

Chen-yu Liu, Da-wei Wang

{"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":null,"pages":null},"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}

引用次数: 2

Weak Multiplex Percolation 弱多重渗流

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-11-03 DOI: 10.1017/9781108865777

G. Baxter, R. da Costa, S. N. Dorogovtsev, J. Mendes

引用次数: 3

Structural signatures for thermodynamic stability in vitreous silica: Insight from machine learning and molecular dynamics simulations 玻璃体二氧化硅热力学稳定性的结构特征:来自机器学习和分子动力学模拟的见解

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-11-02 DOI: 10.1103/PHYSREVMATERIALS.5.015602

Zheng Yu, Qitong Liu, I. Szlufarska, Bu Wang

引用次数: 4

Mean-field model of interacting quasilocalized excitations in glasses 玻璃中相互作用准局域激发的平均场模型

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-10-21 DOI: 10.21468/SCIPOSTPHYSCORE.4.2.008

Corrado Rainone, Eran Bouchbinder, E. Lerner, P. Urbani, F. Zamponi

{"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":null,"pages":null},"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}

引用次数: 19

Signatures of a critical point in the many-body localization transition 多体局部化转换中临界点的特征

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-10-17 DOI: 10.21468/SciPostPhys.10.5.107

'Angel L. Corps, R. Molina, A. Relaño

{"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":null,"pages":null},"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}

引用次数: 10

Entanglement dynamics in the three-dimensional Anderson model 三维Anderson模型中的纠缠动力学

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-10-13 DOI: 10.1103/physrevb.102.195132

Yang Zhao, Dingyi Feng, Yongbo Hu, Shutong Guo, J. Sirker

引用次数: 11

Neural Monte Carlo renormalization group 神经蒙特卡罗重整化群

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-10-12 DOI: 10.1103/PhysRevResearch.3.023230

Jui-Hui Chung, Y. Kao

引用次数: 8

Signatures of many-body localization in the dynamics of two-level systems in glasses 玻璃双能级系统动力学中的多体局部化特征

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-10-07 DOI: 10.1103/PhysRevB.103.214205

Claudia Artiaco, F. Balducci, A. Scardicchio

引用次数: 6

Low-Temperature Thermal and Vibrational Properties of Disordered Solids 无序固体的低温热特性和振动特性

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-10-06 DOI: 10.1142/q0371

A. Grushin

引用次数: 31

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions 具有远程反铁磁相互作用的无序量子自旋链的纠缠特性

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-09-23 DOI: 10.1103/physrevb.102.214201

Y. Mohdeb, J. Vahedi, N. Moure, A. Roshani, Hyunyong Lee, R. Bhatt, S. Kettemann, S. Haas

{"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":null,"pages":null},"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}

引用次数: 3