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In an isolated quantum many-body system undergoing unitary evolution, we study the thermalization of a subsystem, treating the rest of the system as a bath. In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to…

Statistical Mechanics · Physics 2023-11-30 Aram W. Harrow , Yichen Huang

We discuss eigenstate correlations for ergodic, spatially extended many-body quantum systems, in terms of the statistical properties of matrix elements of local observables. While the eigenstate thermalization hypothesis (ETH) is known to…

Statistical Mechanics · Physics 2019-06-11 Amos Chan , Andrea De Luca , J. T. Chalker

The Eigenstate Thermalization Hypothesis (ETH) provides a way to understand how an isolated quantum mechanical system can be approximated by a thermal density matrix. We find a class of operators in (1+1)-$d$ conformal field theories,…

High Energy Physics - Theory · Physics 2017-08-30 Pallab Basu , Diptarka Das , Shouvik Datta , Sridip Pal

The thermalizing dynamics of many-body systems is often described through the lens of the Eigenstate Thermalization Hypothesis (ETH). ETH postulates that the statistical properties of observables, when expressed in the energy eigenbasis,…

Statistical Mechanics · Physics 2026-04-01 Jiaozi Wang , Ruchira Mishra , Tian-Hua Yang , Luca V. Delacrétaz , Silvia Pappalardi

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) insists that for nonintegrable systems each energy eigenstate accurately gives microcanonical expectation values for a class of observables. As a mechanism for ETH to hold, we show that the…

Statistical Mechanics · Physics 2018-05-15 Takaaki Monnai

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,…

Statistical Mechanics · Physics 2025-12-23 Yucheng Wang

The Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in the high energy and condensed matter communities. It explains how an isolated quantum system in a far-from-equilibrium initial state can evolve to a…

Quantum Physics · Physics 2026-04-14 Elena Cáceres , Stefan Eccles , Jason Pollack , Sarah Racz

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

The eigenstate thermalization hypothesis (ETH) is a conjecture on the nature of isolated quantum systems that guarantees the thermal behavior of subsystems when it is satisfied. ETH has been tested in various forms on a number of local…

Statistical Mechanics · Physics 2019-09-18 Masudul Haque , Paul McClarty

The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in…

Statistical Mechanics · Physics 2016-05-04 Pavan Hosur , Xiao-Liang Qi

Isolated quantum systems typically approach thermal equilibrium as described by the Eigenstate Thermalization Hypothesis (ETH). Going beyond this involves either higher order correlators (full thermalization) or the formation of state…

Quantum Physics · Physics 2026-05-01 Tabea Herrmann , Felix Fritzsch , Arnd Bäcker

The eigenstate thermalization hypothesis (ETH) has been highly influential in explaining thermodynamic behavior of closed quantum systems. As of yet, it is unclear whether and how the ETH applies to non-Hermitian systems. Here, we introduce…

Boltzmann's ergodic hypothesis furnishes a possible explanation for the emergence of statistical mechanics in the framework of classical physics. In quantum mechanics, the Eigenstate Thermalization Hypothesis (ETH) is instead generally…

Statistical Mechanics · Physics 2019-04-08 Lorenzo Campos Venuti , Lawrence Liu

The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators. An analog known as the…

Statistical Mechanics · Physics 2024-10-04 Siddharth Jindal , Pavan Hosur

Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical…

Quantum Gases · Physics 2017-07-19 Anatoli Polkovnikov , Dries Sels

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

The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on the relaxation dynamics of observables as…

Quantum Gases · Physics 2020-12-15 Alexander Schuckert , Michael Knap

We investigate the eigenstate thermalization hypothesis (ETH) in integrable models, focusing on the spin-1/2 isotropic Heisenberg (XXX) chain. We provide numerical evidence that ETH holds for typical eigenstates (weak ETH scenario).…

Strongly Correlated Electrons · Physics 2015-04-22 Vincenzo Alba

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