Eigenstate Thermalization Hypothesis and Free Probability
- URL: http://arxiv.org/abs/2204.11679v2
- Date: Tue, 18 Oct 2022 17:46:39 GMT
- Title: Eigenstate Thermalization Hypothesis and Free Probability
- Authors: Silvia Pappalardi, Laura Foini and Jorge Kurchan
- Abstract summary: Quantum thermalization is well understood via the Eigenstate Thermalization Hypothesis (ETH)
In this work, we uncover the close relation between this perspective on ETH and Free Probability theory, as applied to a thermal ensemble or an energy shell.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum thermalization is well understood via the Eigenstate Thermalization
Hypothesis (ETH). The general form of ETH, describing all the relevant
correlations of matrix elements, may be derived on the basis of a `typicality'
argument of invariance with respect to local rotations involving nearby energy
levels. In this work, we uncover the close relation between this perspective on
ETH and Free Probability theory, as applied to a thermal ensemble or an energy
shell. This mathematical framework allows one to reduce in a straightforward
way higher-order correlation functions to a decomposition given by minimal
blocks, identified as free cumulants, for which we give an explicit formula.
This perspective naturally incorporates the consistency property that local
functions of ETH operators also satisfy ETH. The present results uncover a
direct connection between the Eigenstate Thermalization Hypothesis and the
structure of Free Probability, widening considerably the latter's scope and
highlighting its relevance to quantum thermalization.
Related papers
- Consistency of EFT illuminated via relative entropy: A case study in scalar field theory [0.0]
We show that the non-negativity of relative entropy is potentially violated in perturbative calculations.
We revisit an EFT of single-field inflation and present a relation between its non-linear parameter $f_rm NL$ and the consistency condition of the EFT description.
arXiv Detail & Related papers (2024-10-28T14:23:50Z) - Generalized Free Cumulants for Quantum Chaotic Systems [0.0]
The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in isolated quantum systems.
We show that the ETH is a sufficient mechanism for thermalization, in general.
In particular, we show that reduced density matrices relax to their equilibrium form and that systems obey the Page curve at late times.
arXiv Detail & Related papers (2024-01-24T22:04:41Z) - Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization
Hypothesis [0.0]
Eigenstate Thermalization Hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems.
We investigate what extent the ETH holds in non-Hermitian many-body systems.
We come to the surprising conclusion that the fluctuations between eigenstates is of equal order to the average, indicating no thermalization.
arXiv Detail & Related papers (2023-03-06T19:17:15Z) - Accessing the topological Mott insulator in cold atom quantum simulators
with realistic Rydberg dressing [58.720142291102135]
We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices.
We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation.
We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
arXiv Detail & Related papers (2022-03-28T14:55:28Z) - Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems.
This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state.
Our results explain finite-time thermalization in chaotic open quantum systems.
arXiv Detail & Related papers (2021-12-14T18:48:31Z) - Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains
at Finite Temperature: Exact Results [68.8204255655161]
We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures.
The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
arXiv Detail & Related papers (2021-05-11T14:08:02Z) - Exact thermal properties of free-fermionic spin chains [68.8204255655161]
We focus on spin chain models that admit a description in terms of free fermions.
Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
arXiv Detail & Related papers (2021-03-30T13:15:44Z) - Out-of-time-order correlations and the fine structure of eigenstate
thermalisation [58.720142291102135]
Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation.
We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH)
We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
arXiv Detail & Related papers (2021-03-01T17:51:46Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - Does the Eigenstate Thermalization Hypothesis Imply Thermalization? [0.0]
Eigenstate thermalization hypothesis (ETH) is discussed.
We show that one common formulation of ETH does not necessarily imply thermalization of an observable of isolated many body quantum system.
arXiv Detail & Related papers (2020-02-05T16:38:20Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.