Related papers: Does a single eigenstate encode the full Hamiltoni…
We extend the notion of the Eigenstate Thermalization Hypothesis (ETH) to Open Quantum Systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation. We present evidence that the eigenstates of non-equilibrium steady…
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…
Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true…
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,…
We demonstrate that the entanglement entropy area law for free fermion ground states and the corresponding volume law for highly excited states are related by a position-momentum duality, thus of the same origin. For a typical excited state…
Currently there are two main approaches to describe how quantum statistical physics emerges from an isolated quantum many-body system in a pure state: Canonical Typicality (CT) and Eigenstate Thermalization Hypothesis (ETH). These two…
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…
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…
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…
According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated…
Work extraction from the Gibbs ensemble by a cyclic operation is impossible, as represented by the second law of thermodynamics. On the other hand, the eigenstate thermalization hypothesis (ETH) states that just a single energy eigenstate…
Proving thermalization from the unitary evolution of a closed quantum system is one of the oldest questions that is still nowadays only partially resolved. Several efforts have led to various formulations of what is called the eigenstate…
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 provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate…
The strong eigenstate thermalization hypothesis (ETH) provides a sufficient condition for thermalization and equilibration. Although it is expected to be hold in a wide class of highly chaotic theories, there are only a few analytic…
Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes,…
According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit - the…
Complexity of dynamics is at the core of quantum many-body chaos and exhibits a hierarchical feature: higher-order complexity implies more chaotic dynamics. Conventional ergodicity in thermalization processes is a manifestation of the…
We show that macroscopic thermalization and transport impose constraints on matrix elements entering the Eigenstate Thermalization Hypothesis (ETH) ansatz and require them to be correlated. It is often assumed that the ETH reduces to Random…
We study the relative entropy of highly excited quantum states. First, we sample states from the Wishart ensemble and develop a large-N diagrammatic technique for the relative entropy. The solution is exactly expressed in terms of…