Eigenstate plateau transition and equilibration in 1D quantum lattice models

TL;DR

This paper uncovers a spectral phenomenon in 1D quantum lattice models where eigenstates form energy plateaus with phase transition-like gaps, revealing universal dynamics and structural properties relevant to quantum equilibration.

Contribution

It introduces a novel spectral reorganization in quantum lattice models, linking eigenstate structure to out-of-equilibrium dynamics and phase transition-like behavior.

Findings

Eigenstates form energy plateaus with gaps as interaction increases

Structured eigenstates influence universal far-from-equilibrium dynamics

Results are relevant for experimental studies of quantum equilibration

Abstract

We report on a remarkable spectral phenomenon in a generic type of quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize and lead to plateaus of the interaction energy, with gaps opening akin to continuous phase transitions. Perturbation theory identifies a hidden structure underlying eigenstates within each plateau, resulting in a statistical shift in the wavefunction amplitudes described by extreme value theory. The structured eigenstates manifest themselves naturally in far-from-equilibrium dynamics proceeding through multiple universal stages. Our findings reveal a profound connection between emergent properties in high-energy states and out-of-equilibrium dynamics, providing insights into the impact of interactions across the entire energy spectrum. The results are directly relevant to experiments probing equilibration in quantum spin and lattice gases.