Eigenstate thermalization and spectral imprints of many-body systems in projected local observables
Phys. Rev. B 114, 034202 – Published 6 July, 2026
DOI: https://doi.org/10.1103/d87q-hwqw
Abstract
The Eigenstate Thermalization Hypothesis explains thermalization in isolated quantum systems through the statistical properties of observables in the energy eigenbasis. We study the crossover from integrability-to-chaos in the spin- XXZ chain by introducing a local perturbation. Using exact diagonalization, we characterize this crossover through spectral correlations, standard ETH indicators, and eigenstate entanglement entropy. Beyond these conventional probes, we introduce a submatrix-based framework in which local observables are projected onto contiguous energy windows along the diagonal of their representation in the Hamiltonian eigenbasis. The resulting real-symmetric submatrices exhibit a banded matrixlike structure and display both short-range and long-range spectral correlations similar to those of the Hamiltonian. Remarkably, this resemblance between the spectral statistics of the Hamiltonian and those of the submatrices persists even in intermediate regimes that are not fully chaotic, suggesting that signatures of the integrability-to-chaos crossover are reflected in collective correlations among observable matrix elements, even when the system is not fully ergodic.
