Numerical evidence for the non-Abelian eigenstate thermalization hypothesis

• URL: http://arxiv.org/abs/2412.07838v1
• Date: Tue, 10 Dec 2024 19:00:01 GMT
• Title: Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
• Authors: Aleksander Lasek, Jae Dong Noh, Jade LeSchack, Nicole Yunger Halpern,
• Abstract summary: The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally. We prove analytically that the non-Abelian ETH exhibits a self-consistency property.
• Score: 41.94295877935867
• License:
• Abstract: The eigenstate thermalization hypothesis (ETH) explains how generic quantum many-body systems thermalize internally. It implies that local operators' time-averaged expectation values approximately equal their thermal expectation values, regardless of microscopic details. The ETH's range of applicability therefore impacts theory and experiments. Murthy $\textit{et al.}$ recently showed that non-Abelian symmetries conflict with the ETH. Such symmetries have excited interest in quantum thermodynamics lately, as they are equivalent to conserved quantities that fail to commute with each other and noncommutation is a quintessentially quantum phenomenon. Murthy $\textit{et al.}$ proposed a non-Abelian ETH, which we support numerically. The numerics model a one-dimensional (1D) next-nearest-neighbor Heisenberg chain of up to 18 qubits. We represent local operators with matrices relative to an energy eigenbasis. The matrices bear out seven predictions of the non-Abelian ETH. We also prove analytically that the non-Abelian ETH exhibits a self-consistency property. The proof relies on a thermodynamic-entropy definition different from that in Murthy $\textit{et al.}$ This work initiates the observation and application of the non-Abelian ETH.

Related papers

• Remarks on effects of projective phase on eigenstate thermalization hypothesis [0.0]
  We consider $mathbbZ_NtimesmathbbZ_N$ symmetries with nontrivial projective phases. We also perform numerical analyses for $ (1+1)$-dimensional spin chains and the $ (2+1)$-dimensional lattice gauge theory.
  arXiv  Detail & Related papers  (2023-10-17T17:36:37Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Bounds on eigenstate thermalization [8.329456268842227]
  The eigenstate thermalization hypothesis (ETH) asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble. Here, we show the existence of upper and lower bounds on $m_ast$ such that all $m$-body operators with $m m_ast$ satisfy the ETH. Our results imply that generic systems satisfy the ETH for any few-body operators, including their thermal and quantum fluctuations.
  arXiv  Detail & Related papers  (2023-03-17T15:52:08Z)
• 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)
• Non-Abelian eigenstate thermalization hypothesis [58.720142291102135]
  The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics.
  arXiv  Detail & Related papers  (2022-06-10T18:14:18Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• 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)
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions [0.0]
  Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz. We study a quantum chaotic spin-fermion model in a one-dimensional lattice.
  arXiv  Detail & Related papers  (2020-11-27T19:05:32Z)
• 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.