Related papers: Eigenstate Thermalization and Spectral Imprints of the Hamiltonian in Local Observables

Eigenstate Thermalization and Spectral Imprints of the Hamiltonian in Local Observables

URL: http://arxiv.org/abs/2601.09340v1
Date: Wed, 14 Jan 2026 10:15:50 GMT
Title: Eigenstate Thermalization and Spectral Imprints of the Hamiltonian in Local Observables
Authors: Shivam Mishra, C Jisha, Ravi Prakash,
Abstract summary: Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems.<n>We investigate the crossover from integrability to chaos in the spin-$1/2$ XXZ chain.<n>By introducing a local perturbation that drives the system from integrability to chaos, we track the standard ETH indicators and the eigenstate entanglement entropy.
Score: 1.4474137122906165
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We investigate the crossover from integrability to chaos in the spin-$1/2$ XXZ chain, establishing a direct correspondence between the spectral correlations of the Hamiltonian and local observables expressed in the energy eigenbasis as a signature of ergodicity breaking. By introducing a local perturbation that drives the system from integrability to chaos, we track the standard ETH indicators and the eigenstate entanglement entropy. We introduce a submatrix-based framework for analyzing local observables in the energy eigenbasis. By extracting real-symmetric blocks along the diagonal of the local observables represented in eigenbasis, we show that these submatrices exhibit both the short-range and long-range spectral features of the Hamiltonian. Remarkably, this correspondence persists even in a partially ergodic regime, indicating that the emergence of chaos is already encoded locally within the observables' matrix structure and that small blocks are sufficient to capture the underlying spectral correlations.

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