Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies.

  title={Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies.},
  author={Jonas Richter and Anatoly Dymarsky and Robin Steinigeweg and Jochen Gemmer},
  journal={Physical review. E},
  volume={102 4-1},
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between… 
Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations.
  • J. Noh
  • Physics
    Physical review. E
  • 2021
The self-averaging behavior indicates that the energy eigenstates are statistically equivalent to each other, which is consistent with the ETH, and explains the origin for the breakdown of the fluctuation dissipation theorem in the integrable system.
Eigenstate thermalization hypothesis through the lens of autocorrelation functions
Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz within the eigenstate thermalization hypothesis (ETH). We study a quantum chaotic
Typical perturbation theory: conditions, accuracy and comparison with a mesoscopic case
The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while
Tight-binding billiards
Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common
Thermalization of locally perturbed many-body quantum systems
Deriving conditions under which a macroscopic system thermalizes directly from the underlying quantum many-body dynamics of its microscopic constituents is a long-standing challenge in theoretical
OPE statistics from higher-point crossing
Abstract We present new asymptotic formulas for the distribution of OPE coefficients in conformal field theories. These formulas involve products of four or more coefficients and include
Non-Gaussianities in the statistical distribution of heavy OPE coefficients and wormholes
This paper investigates non- Gaussian corrections to the statistical distribution of heavy-heavy-heavy OPE coefficients in chaotic two-dimensional conformal field theories and suggests that there are new connected wormhole geometries that dominate over the genus-two wormhole.
Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with
Random matrix theory for complexity growth and black hole interiors
We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional


A 37
  • 4723
  • 2004
  • Rev. E 100, 062134
  • 2019
  • Thomas de Quincey
  • Physics
    The Works of Thomas De Quincey, Vol. 1: Writings, 1799–1820
  • 2000
In supernova (SN) spectroscopy relatively little attention has been given to the properties of optically thick spectral lines in epochs following the photosphere’s recession. Most treatments and
Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
We study the matrix elements of local operators in the eigenstates of the integrable XXZ chain and of the quantum-chaotic model obtained by locally perturbing the XXZ chain with a magnetic impurity.
Speck of chaos
It has been shown that a local perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. Here, we
Eigenstate Thermalization in a Locally Perturbed Integrable System.
It is shown that the diagonal matrix elements of observables in the perturbed eigenstates follow the microcanonical predictions for the integrable model, and that the ballistic character of spin transport in the integRable model is manifest in the behavior of the off-diagonal matrix element of the current operator in the probabilistic eigenstate.
Entanglement and matrix elements of observables in interacting integrable systems.
The bipartite von Neumann entanglement entropy and matrix elements of local operators in the eigenstates of an interacting integrable Hamiltonian (the paradigmatic spin-1/2 XXZ chain) are studied, and it is found that the leading term of the average eigenstate entanglements has a volume-law coefficient that is smaller than the universal one in quantum chaotic systems.
Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems.
The relationship between heating rates and the smooth function that characterizes the off-diagonal matrix elements of the drive operator in the eigenbasis of the static Hamiltonian is discussed and it is shown that such a function, in nonintegrable and (remarkably) integrable Hamiltonians, can be probed experimentally by studying heating rates as functions of theDrive frequency.
Bounds on Chaos from the Eigenstate Thermalization Hypothesis.
We show that the known bound on the growth rate of the out-of-time-order four-point correlator in chaotic many-body quantum systems follows directly from the general structure of operator matrix
Exponential damping induced by random and realistic perturbations.
This work studies the decay of current autocorrelation functions in spin-1/2 ladder systems and finds a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.