Related papers: Degenerate observables and the many Eigenstate The…
It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive, since there are systems that are asymptotically in a thermal…
We study the emergence of statistical mechanics in isolated classical systems with local interactions and discrete phase spaces. We establish that thermalization in such systems does not require global ergodicity; instead, it arises from…
In a recent Letter [PhysRevLett.119.030601 (2017), arXiv:1702.08227], Shiraishi and Mori claim to provide a general method for constructing local Hamiltonians that do not exhibit eigenstate thermalization. We argue that the claim is based…
For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that…
We propose a generalization of the eigenstate thermalization hypothesis accounting for the emergence of symmetry-breaking phases. It consists of two conditions that any system with a degenerate spectrum must fulfill in order to thermalize.…
The Eigenstate Thermalization Hypothesis (ETH) is a framework for discussing thermal behavior originating from chaotic dynamics in isolated many-body quantum systems. The PXP model, where certain states do not thermalize, has been compared…
By calculating correlation functions for the Lieb-Liniger model based on the algebraic Bethe ansatz method, we conduct a finite-size scaling analysis of the eigenstate thermalization hypothesis (ETH) which is considered to be a possible…
To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. Despite the fact that the theory is more than 100 years old, we are still discussing its foundations…
We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that…
The Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. Only recently has the attention been paid to so-called full ETH, which accounts for higher-order…
We initiate a systematic study of high energy matrix elements of local operators in 2d CFT. Knowledge of these is required in order to determine whether the eigenstate thermalization hypothesis (ETH) can hold in such theories. Most high…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
We compute exactly the von Neumann entanglement entropy of the eta-pairing states - a large set of exact excited eigenstates of the Hubbard Hamiltonian. For the singlet eta-pairing states the entropy scales with the logarithm of the spatial…
Generalized thermalization is a process that occurs in integrable systems in which unitary dynamics, e.g., following a quantum quench, results in states in which observables after equilibration are described by generalized Gibbs ensembles…
We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite…
The eigenstate thermalization hypothesis as well as the quantum ergodic theorem are studied in the light of quantum Fisher information. We show how global bounds on quantum Fisher information set the ETH and ergodicity conditions.…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
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…
Unitary Designs have become a vital tool for investigating pseudorandomness since they approximate the statistics of the uniform Haar ensemble. Despite their central role in quantum information, their relation to quantum chaotic evolution…
We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization…