Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis

TL;DR

This study investigates how initial state independent equilibration and quantum chaos relate in asymmetric Heisenberg spin ladders, revealing ETH violations and a transition to integrability at strong interactions through numerical analysis.

Contribution

It demonstrates the violation of ETH at high interaction strengths and links this to a transition from chaotic to integrable behavior in quantum spin ladders.

Findings

ETH is violated at large interaction strengths.

Level statistics transition from Poisson to Wigner distribution.

Energy difference relaxation depends on the interaction strength.

Abstract

This work aims at understanding the interplay between the Eigenstate Thermalization Hypothesis (ETH), initial state independent equilibration and quantum chaos in systems that do not have a direct classical counterpart. It is based on numerical investigations of asymmetric Heisenberg spin ladders with varied interaction strengths between the legs, i.e., along the rungs. The relaxation of the energy difference between the legs is investigated. Two different parameters, both intended to quantify the degree of accordance with the ETH, are computed. Both indicate violation of the ETH at large interaction strengths but at different thresholds. Indeed the energy difference is found not to relax independently of its initial value above some critical interaction strength which coincides with one of the thresholds. At the same point the level statistics shift from Poisson-type to Wigner-type. Hence the system may be considered to become integrable again in the strong interaction limit.