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We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-flip dynamics, the Hilbert space, which…

Statistical Mechanics · Physics 2017-09-25 Zhihao Lan , Stephen Powell

We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the…

Mathematical Physics · Physics 2021-07-01 Zhigang Bao , Laszlo Erdos , Kevin Schnelli

Motivated by the qualitative picture of Canonical Typicality, we propose a refined formulation of the Eigenstate Thermalization Hypothesis (ETH) for chaotic quantum systems. The new formulation, which we refer to as subsystem ETH, is in…

Statistical Mechanics · Physics 2018-04-06 Anatoly Dymarsky , Nima Lashkari , Hong Liu

We consider the quadratic form of a general deterministic matrix on the eigenvectors of an $N\times N$ Wigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large $N$ limit. The proof is a combination of…

Probability · Mathematics 2022-03-04 Giorgio Cipolloni , László Erdős , Dominik Schröder

An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von…

Statistical Mechanics · Physics 2012-03-15 Marcos Rigol , Mark Srednicki

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…

Statistical Mechanics · Physics 2025-12-01 Elisa Vallini , Laura Foini , Silvia Pappalardi

Eigenstate thermalization is widely accepted as the mechanism behind thermalization in generic isolated quantum systems. Using the example of a single magnetic defect embedded in the integrable spin-1/2 $XXZ$ chain, we show that locally…

Statistical Mechanics · Physics 2020-08-14 Marlon Brenes , Tyler LeBlond , John Goold , Marcos Rigol

The Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. However, its connection to the timescale of thermalization for open system dynamics has remained…

Quantum Physics · Physics 2023-03-30 Chi-Fang Chen , Fernando G. S. L. Brandão

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…

Statistical Mechanics · Physics 2018-02-27 Ryusuke Hamazaki , Masahito Ueda

Understanding how an isolated quantum system evolves toward a thermal state from an initial state far from equilibrium such as one prepared by a global quantum quench has attracted significant interest in recent years. This phenomenon can…

High Energy Physics - Theory · Physics 2025-01-23 Mohsen Alishahiha , Mohammad Javad Vasli

The eigenstate thermalization hypothesis (ETH) is a successful theory that establishes the criteria for ergodicity and thermalization in isolated quantum many-body systems. In this work, we investigate the thermalization properties of…

The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi-)energy…

Statistical Mechanics · Physics 2021-06-30 Felix Fritzsch , Tomaž Prosen

The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate…

Statistical Mechanics · Physics 2026-05-11 Pavel Orlov , Rustem Sharipov , Enej Ilievski

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of…

Statistical Mechanics · Physics 2026-01-14 Maksym Serbyn , Alexander Avdoshkin , Oriana K. Diessel , David A. Huse

The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the…

Quantum Physics · Physics 2026-01-15 Shivam Mishra , C Jisha , Ravi Prakash

We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…

Mathematical Physics · Physics 2015-05-18 Laszlo Erdos

The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum…

Statistical Mechanics · Physics 2025-05-27 Shoki Sugimoto , Ryusuke Hamazaki , Masahito Ueda

We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in…

High Energy Physics - Theory · Physics 2010-02-16 G. Akemann , E. Bittner , M. J. Phillips , L. Shifrin

A strongly non-integrable system is expected to satisfy the eigenstate thermalization hypothesis, which states that the expectation value of an observable in an energy eigenstate is the same as the thermal value. This must be revised if the…

Statistical Mechanics · Physics 2015-11-04 Keith R. Fratus , Mark Srednicki

We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. Under suitable…

Mathematical Physics · Physics 2009-05-13 Laszlo Erdos , Benjamin Schlein , Horng-Tzer Yau