Predicting dynamics from flows of the eigenstate thermalization hypothesis
5 affiliations
- 1Clarendon Laboratory
- 2Max Planck Institute for the Physics of Complex Systems
- 3University of Maryland, College Park
- 4Stanford University
- 5Boston University
Abstract
Analytical treatments of far-from-equilibrium quantum dynamics are few, even in well-thermalizing systems. The celebrated eigenstate thermalization hypothesis (ETH) provides a ansatz for the matrix elements of observables in the eigenbasis of a thermalizing Hamiltonian, given various response functions of those observables as input. However, the ETH cannot predict these response functions. We introduce a procedure, dubbed the statistical Jacobi approximation (SJA), to update the ETH ansatz after a perturbation to the Hamiltonian and predict perturbed response functions. The Jacobi algorithm diagonalizes the perturbation through a sequence of two-level rotations. The SJA implements these rotations statistically assuming the ETH throughout the diagonalization procedure and generates integrodifferential flow equations for various form factors in the ETH ansatz. We approximately solve these flow equations using statistical information about Jacobi rotations as input and predict both quench dynamics and autocorrelators in the thermal state of the perturbed Hamiltonian. The predicted dynamics agree with exact numerics in both random matrix models and spin chains, outperforming second-order time-dependent perturbation theory.
Versions
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BibTeX
@article{hahn2026predicting,
title = {{Predicting dynamics from flows of the eigenstate thermalization hypothesis}},
author = {Dominik Hahn and David M. Long and Marin Bukov and Anushya Chandran},
journal = {Physical Review Research},
year = {2026},
month = oct,
doi = {10.1103/c9d7-x8gc},
url = {http://link.aps.org/doi/10.1103/c9d7-x8gc},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Predicting dynamics from flows of the eigenstate thermalization hypothesis
AU - Dominik Hahn
AU - David M. Long
AU - Marin Bukov
AU - Anushya Chandran
PY - 2026
DA - 2026/10/23
JO - Physical Review Research
DO - 10.1103/c9d7-x8gc
UR - http://link.aps.org/doi/10.1103/c9d7-x8gc
AB - Analytical treatments of far-from-equilibrium quantum dynamics are few, even in well-thermalizing systems. The celebrated eigenstate thermalization hypothesis (ETH) provides a ansatz for the matrix elements of observables in the eigenbasis of a thermalizing Hamiltonian, given various response functions of those observables as input. However, the ETH cannot predict these response functions. We introduce a procedure, dubbed the statistical Jacobi approximation (SJA), to update the ETH ansatz after a perturbation to the Hamiltonian and predict perturbed response functions. The Jacobi algorithm diagonalizes the perturbation through a sequence of two-level rotations. The SJA implements these rotations statistically assuming the ETH throughout the diagonalization procedure and generates integrodifferential flow equations for various form factors in the ETH ansatz. We approximately solve these flow equations using statistical information about Jacobi rotations as input and predict both quench dynamics and autocorrelators in the thermal state of the perturbed Hamiltonian. The predicted dynamics agree with exact numerics in both random matrix models and spin chains, outperforming second-order time-dependent perturbation theory.
SN - 2643-1564
ER -