On eigenstate thermalization in the SYK chain model
- URL: http://arxiv.org/abs/2104.05291v1
- Date: Mon, 12 Apr 2021 08:50:24 GMT
- Title: On eigenstate thermalization in the SYK chain model
- Authors: Seyyed M.H. Halataei
- Abstract summary: Eigenstate thermalization hypothesis (ETH) explains how generic observables of individual isolated quantum systems in pure states can exhibit thermal behaviors.
We show that for two conventional few-body operators, the ensemble-averaged theory of the SYK chain model strictly satisfies ETH conditions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Eigenstate thermalization hypothesis (ETH) explains how generic observables
of individual isolated quantum systems in pure states can exhibit thermal
behaviors. ETH ansatz usually holds true in quantum chaotic systems. In this
paper, we examine a one-dimensional lattice generalization of the
Sachdev-Ye-Kitaev model with spatial local random interaction of Majorana
fermions, the so-called SYK chain model. The model is maximally chaotic but its
R\'enyi entanglement entropy study suggests that the model does not rapidly
thermalize. We show, however, that for two conventional few-body operators, the
ensemble-averaged theory of the SYK chain model strictly satisfies ETH
conditions. We also demonstrate that for every single realization of the
ensemble, the operators loosely satisfy ETH, and consequently rapidly
thermalize, albeit, with larger fluctuations. We comment on the difference
between the application of ETH for individual systems and ensemble-averaged
ones. We also use our results to comment on the implications for eigenstate
correlation functions and a putative gravitational dual theory.
Related papers
- Generic ETH: Eigenstate Thermalization beyond the Microcanonical [0.0]
Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in high energy and condensed matter communities.
We design a qutrit lattice system with conserved quasilocal charge, in which we verify a form of generalized eigenstate thermalization.
We also observe prototypical signatures of thermalization in states well outside microcanonical windows of both charge and energy, which we dub generic ETH'
arXiv Detail & Related papers (2024-03-08T10:19:04Z) - 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) - Thermodynamics and dynamics of coupled complex SYK models [0.0]
This work establishes the universality of this shared universality class and chaotic properties for SYK-like models.
We demonstrate that the coupled SYK system remains maximally chaotic in the large-$q$ limit at low temperatures.
These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems.
arXiv Detail & Related papers (2023-12-22T12:26:42Z) - Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it.
We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
arXiv Detail & Related papers (2023-06-16T16:41:16Z) - 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) - New insights on the quantum-classical division in light of Collapse
Models [63.942632088208505]
We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases.
A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
arXiv Detail & Related papers (2022-10-19T14:51:21Z) - 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) - 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)
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.