Related papers: Off-Diagonal Observable Elements from Random Matri…
Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the…
The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal…
We verify that the eigenstate thermalization hypothesis (ETH) holds universally for locally interacting quantum many-body systems. Introducing random-matrix ensembles with interactions, we numerically obtain a distribution of maximum…
The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…
The Eigenstate Thermalization Hypothesis (ETH) was developed as a framework for understanding how the principles of statistical mechanics emerge in the long-time limit of isolated quantum many-body systems. Since then, ETH has shifted the…
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 spin-fermion model in a one-dimensional lattice,…
The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems, yet a complete and conceptually transparent derivation has remained elusive. In this work,…
If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is…
Understanding how out-of-equilibrium states thermalize under quantum unitary dynamics is an important problem in many-body physics. In this work, we propose a statistical ansatz for the matrix elements of non-equilibrium initial states in…
The Eigenstate Thermalization Hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. The ETH asserts that expectation values of simple observables in energy…
To bypass the reliance on local observables in verifying the eigenstate thermalization hypothesis (ETH), we introduce an observable-independent measure of distinguishability based on the variance of a rescaled local operator. We establish a…
We investigate off-diagonal matrix elements of local operators in integrable spin chains, focusing on the isotropic spin-$1/2$ Heisenberg chain ($XXX$ chain). We employ state-of-the-art Algebraic Bethe Ansatz results, which allow us to…
We report an example of a many-body system, derived from the double kicked top (DKT), with non-chaotic yet mean-ergodic dynamics that displays \textit{strong} eigenstate thermalization hypothesis (ETH) in the quantum regime. The analysis…
The eigenstate thermalization hypothesis (ETH) describes the properties of diagonal and off-diagonal matrix elements of local operators in the eigenenergy basis. In this work, we propose a relation between (i) the singular behaviour of the…
Even though foundations of the eigenstate thermalization hypothesis (ETH) are based on random matrix theory, physical Hamiltonians and observables substantially differ from random operators. One of the major challenges is to embed local…
This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of…
The eigenstate thermalization hypothesis (ETH), which dictates that all diagonal matrix elements within a small energy shell be almost equal, is a major candidate to explain thermalization in isolated quantum systems. According to the…
In this paper, we investigate the distinctions between realistic quantum chaotic systems and random models from the perspective of observable properties, particularly focusing on the eigenstate thermalization hypothesis (ETH). Through…
The Eigenstate Thermalization Hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems. Another signal of chaos is a positive Lyapunov…
The emergence of statistical mechanics for isolated classical systems comes about through chaotic dynamics and ergodicity. Here we review how similar questions can be answered in quantum systems. The crucial point is that individual energy…