arXiv: Statistical Mechanics最新文献_第3页

Spectral Lyapunov exponents in chaotic and localized many-body quantum systems 混沌和定域多体量子系统中的谱Lyapunov指数

arXiv: Statistical Mechanics Pub Date : 2020-12-09 DOI: 10.1103/PhysRevResearch.3.023118

Amos Chan, A. De Luca, J. Chalker

{"title":"Spectral Lyapunov exponents in chaotic and localized many-body quantum systems","authors":"Amos Chan, A. De Luca, J. Chalker","doi":"10.1103/PhysRevResearch.3.023118","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.3.023118","url":null,"abstract":"We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized phases (MBL). The spectral statistics are characterized by the traces of powers $t$ of the Floquet operator, and our approach hinges on the fact that, for integer $t$ in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call textit{spectral Lyapunov exponents}. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block-diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large $t$ we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension $q$ in the large-$q$ limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of non-interacting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher point spectral form factors (hpSFF) in the large-$q$ limit, and show that the generalized Thouless time scales logarithmically in system size for all hpSFF in the large-$q$ chaotic phase.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80693461","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: 24

Effective free-fermionic form factors and the XY spin chain 有效自由费米子形状因子和XY自旋链

arXiv: Statistical Mechanics Pub Date : 2020-12-03 DOI: 10.21468/SCIPOSTPHYS.10.3.070

O. Gamayun, N. Iorgov, Y. Zhuravlev

引用次数: 13

Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases 双层Haldane体系:拓扑表征及连接Chern相的绝热通道

arXiv: Statistical Mechanics Pub Date : 2020-12-02 DOI: 10.1103/PhysRevB.103.224304

S. Bhattacharjee, Souvik Bandyopadhyay, D. Sen, A. Dutta

引用次数: 0

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization O(N)$模型的非扰动重整化临界指数的分析性

arXiv: Statistical Mechanics Pub Date : 2020-12-01 DOI: 10.21468/SciPostPhys.10.6.134

A. Chlebicki, P. Jakubczyk

{"title":"Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization","authors":"A. Chlebicki, P. Jakubczyk","doi":"10.21468/SciPostPhys.10.6.134","DOIUrl":"https://doi.org/10.21468/SciPostPhys.10.6.134","url":null,"abstract":"We employ the functional renormalization group framework at second order in the derivative expansion to study the $O(N)$ models continuously varying the number of field components $N$ and the spatial dimensionality $d$. Of our special interest are phenomena occurring in the vicinity of $d=2$. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents $nu$ and $eta$ across a line in the $(d,N)$ plane, which passes through the point $(2,2)$. By direct numerical evaluation of $eta(d,N)$ and $nu^{-1}(d,N)$ we find no evidence of discontinuous or singular first and second derivatives of these functions for $d>2$. The computed derivatives of $eta(d,N)$ and $nu^{-1}(d,N)$ become increasingly large for $dto 2$ and $Nto 2$ and it is only in this limit that $eta(d,N)$ and $nu^{-1}(d,N)$ as obtained by us are evidently nonanalytical. The derivatives of the exponents show, nonetheless, a locus of maxima located along a line in the $(d,N)$-plane, with magnitude controlled by the distance from the point $(d,N)=(2,2)$. This locus is situated close to the expected position of the Cardy-Hamber nonanalyticity line. We provide a discussion of the evolution of the obtained picture upon varying $d$ and $N$ between $(d,N)=(2,2)$ and other, earlier studied cases, such as $dto 3$ or $Nto infty$.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89409218","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: 8

Time-dependent self-consistent harmonic approximation: Anharmonic nuclear quantum dynamics and time correlation functions 时变自洽调和近似:非调和核量子动力学与时间相关函数

arXiv: Statistical Mechanics Pub Date : 2020-11-30 DOI: 10.1103/PHYSREVB.103.104305

Lorenzo Monacelli, F. Mauri

{"title":"Time-dependent self-consistent harmonic approximation: Anharmonic nuclear quantum dynamics and time correlation functions","authors":"Lorenzo Monacelli, F. Mauri","doi":"10.1103/PHYSREVB.103.104305","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.104305","url":null,"abstract":"Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, fully accounting for the quantum nature of the nuclei and the anharmonicity in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximated theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical correlation functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the method on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89745970","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: 12

Emergent fracton dynamics in a nonplanar dimer model 非平面二聚体模型中的涌现分形动力学

arXiv: Statistical Mechanics Pub Date : 2020-11-19 DOI: 10.1103/PHYSREVB.103.094303

J. Feldmeier, F. Pollmann, M. Knap

{"title":"Emergent fracton dynamics in a nonplanar dimer model","authors":"J. Feldmeier, F. Pollmann, M. Knap","doi":"10.1103/PHYSREVB.103.094303","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.094303","url":null,"abstract":"We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable automata circuits unveils a rich phenomenology of the system's non-equilibrium properties: For a large class of relevant initial states, local charges are effectively restricted to move along one-dimensional 'tubes' within the quasi-two-dimensional system, displaying fracton-like mobility constraints. The time scale on which these tubes are stable diverges with increasing systems size, yielding a novel mechanism for non-ergodic behavior in the thermodynamic limit. We further explore the role of geometry by studying the system in a quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due to the emergence of an extensive number of conserved quantities. This provides an instance of a recently introduced concept of 'statistically localized integrals of motion', whose universal anomalous hydrodynamics we determine by a mapping to a problem of classical tracer diffusion. We conclude by discussing how our approach might generalize to study transport in other lattice gauge theories.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82051550","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: 13

Diffusion with local resetting and exclusion 扩散与局部重置和排除

arXiv: Statistical Mechanics Pub Date : 2020-11-16 DOI: 10.1103/PHYSREVRESEARCH.3.L012023

Asaf Miron, S. Reuveni

引用次数: 14

Exact many-body scars and their stability in constrained quantum chains 精确的多体伤痕及其在受限量子链中的稳定性

arXiv: Statistical Mechanics Pub Date : 2020-11-16 DOI: 10.1103/PHYSREVB.103.104302

F. Surace, Matteo Votto, Eduardo Gonzalez Lazo, Alessandro Silva, M. Dalmonte, G. Giudici

引用次数: 29

Operator growth in a quantum compass model on a Bethe lattice 贝特晶格上量子罗盘模型中的算子增长

arXiv: Statistical Mechanics Pub Date : 2020-11-14 DOI: 10.1103/PhysRevB.103.L201108

X. Zotos

引用次数: 2

Integrable nonunitary open quantum circuits 可积非酉开量子电路

arXiv: Statistical Mechanics Pub Date : 2020-11-12 DOI: 10.1103/PHYSREVB.103.115132

Lucas Sá, P. Ribeiro, T. Prosen

引用次数: 24