Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos

被引:213
作者
Bertini, Bruno [1 ]
Kos, Pavel [1 ]
Prosen, Tomaz [1 ]
机构
[1] Univ Ljubljana, Fac Math & Phys, Dept Phys, Jadranska 19, SI-1000 Ljubljana, Slovenia
关键词
SYSTEM;
D O I
10.1103/PhysRevLett.121.264101
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transform of spectral density's two-point function, the spectral form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the spectral form factor is demonstrated to match RMT for all values of the integer time variable t in the thermodynamic limit. In particular, we rigorously prove RMT form factor for an odd t, while we formulate a precise conjecture for an even t. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in nonintegrable systems.
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页数:6
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共 40 条
  • [1] Particle-time duality in the kicked Ising spin chain
    Akila, M.
    Waltner, D.
    Gutkin, B.
    Guhr, T.
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (37)
  • [2] Semiclassical Identification of Periodic Orbits in a Quantum Many-Body System
    Akila, Maram
    Waltner, Daniel
    Gutkin, Boris
    Braun, Petr
    Guhr, Thomas
    [J]. PHYSICAL REVIEW LETTERS, 2017, 118 (16)
  • [3] Matrix Product States for Dynamical Simulation of Infinite Chains
    Banuls, M. C.
    Hastings, M. B.
    Verstraete, F.
    Cirac, J. I.
    [J]. PHYSICAL REVIEW LETTERS, 2009, 102 (24)
  • [4] LEVEL CLUSTERING IN REGULAR SPECTRUM
    BERRY, MV
    TABOR, M
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1977, 356 (1686): : 375 - 394
  • [6] QUANTIZING A CLASSICALLY ERGODIC SYSTEM - SINAI BILLIARD AND THE KKR METHOD
    BERRY, MV
    [J]. ANNALS OF PHYSICS, 1981, 131 (01) : 163 - 216
  • [7] CHARACTERIZATION OF CHAOTIC QUANTUM SPECTRA AND UNIVERSALITY OF LEVEL FLUCTUATION LAWS
    BOHIGAS, O
    GIANNONI, MJ
    SCHMIT, C
    [J]. PHYSICAL REVIEW LETTERS, 1984, 52 (01) : 1 - 4
  • [8] ON THE CONNECTION BETWEEN QUANTIZATION OF NON-INTEGRABLE SYSTEMS AND STATISTICAL-THEORY OF SPECTRA
    CASATI, G
    VALZGRIS, F
    GUARNIERI, I
    [J]. LETTERE AL NUOVO CIMENTO, 1980, 28 (08): : 279 - 282
  • [9] Solution of a Minimal Model for Many-Body Quantum Chaos
    Chan, Amos
    De Luca, Andrea
    Chalker, J. T.
    [J]. PHYSICAL REVIEW X, 2018, 8 (04):
  • [10] Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems
    Chan, Amos
    De Luca, Andrea
    Chalker, J. T.
    [J]. PHYSICAL REVIEW LETTERS, 2018, 121 (06)