Random-matrix and transport frequencies in eigenstate spectral functions
Abstract
The fact that generic isolated many-body quantum systems thermalize is understood using the eigenstate thermalization hypothesis (ETH). In recent years, there has been much interest in the behavior of the ETH spectral functions, which characterize the smooth dependence of the variance of the off-diagonal matrix elements of observables on the associated energy and frequency, and whose low-frequency part contains information about the long-time dynamics. In finite systems described by the ETH, the spectral functions are expected to exhibit plateaus below a characteristic frequency ωETH. In this regime, the statistics of the matrix elements of observables are expected to be described by random matrix theory. Related frequencies that have been studied in the literature are ωSFF, which controls the onset of random-matrix behavior in the spectral form factor, and the transport frequencies ωtr, which are derived from transport coefficients. However, a direct quantitative comparison of these frequencies is lacking. Using exact diagonalization, we conduct such a comparison for the spectral functions of current operators in clean and disordered quantum spin ladders with diffusive energy and spin transport. We find clear evidence for the expected low-frequency plateaus in the ETH spectral functions. For the accessible system sizes, ωSFF is consistent with the extent of the plateaus, while the transport frequencies are systematically larger and lie in the nonuniversal regime of the spectral functions. Our findings highlight the need to better understand the origin of these quantitative differences.
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BibTeX
@misc{ceven2026randommatrix,
title = {{Random-matrix and transport frequencies in eigenstate spectral functions}},
author = {Kadir Çeven and Rohit Patil and Marcos Rigol and Fabian Heidrich-Meisner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24602},
eprint = {2609.24602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24602},
}
RIS
TY - UNPB
TI - Random-matrix and transport frequencies in eigenstate spectral functions
AU - Kadir Çeven
AU - Rohit Patil
AU - Marcos Rigol
AU - Fabian Heidrich-Meisner
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24602
UR - https://arxiv.org/abs/2609.24602
AB - The fact that generic isolated many-body quantum systems thermalize is understood using the eigenstate thermalization hypothesis (ETH). In recent years, there has been much interest in the behavior of the ETH spectral functions, which characterize the smooth dependence of the variance of the off-diagonal matrix elements of observables on the associated energy and frequency, and whose low-frequency part contains information about the long-time dynamics. In finite systems described by the ETH, the spectral functions are expected to exhibit plateaus below a characteristic frequency ω^_ETH. In this regime, the statistics of the matrix elements of observables are expected to be described by random matrix theory. Related frequencies that have been studied in the literature are ω^_SFF, which controls the onset of random-matrix behavior in the spectral form factor, and the transport frequencies ω^_tr, which are derived from transport coefficients. However, a direct quantitative comparison of these frequencies is lacking. Using exact diagonalization, we conduct such a comparison for the spectral functions of current operators in clean and disordered quantum spin ladders with diffusive energy and spin transport. We find clear evidence for the expected low-frequency plateaus in the ETH spectral functions. For the accessible system sizes, ω^_SFF is consistent with the extent of the plateaus, while the transport frequencies are systematically larger and lie in the nonuniversal regime of the spectral functions. Our findings highlight the need to better understand the origin of these quantitative differences.
ER -