Quasi-Adiabatic Processing of Thermal States

TL;DR

This paper explores the effectiveness of quasi-adiabatic evolution protocols starting from finite-temperature Gibbs states, establishing benchmarks for success and analyzing their convergence in quantum many-body systems.

Contribution

It introduces new metrics to quantify off-diagonal contributions and demonstrates their convergence properties analytically and numerically in specific quantum models.

Findings

Benchmarks for adiabatic evolution success converge polynomially with time and system size.

Off-diagonality metrics effectively indicate the approach to ideal adiabatic states.

Numerical results show good agreement with analytical predictions in non-integrable systems.

Abstract

We investigate the performance of an adiabatic evolution protocol when initialized from a Gibbs state at finite temperature. Specifically, we identify the diagonality of the final state in the energy eigenbasis, as well as the difference in energy and in energy variance with respect to the ideal adiabatic limit as key benchmarks for success and introduce metrics to quantify the off-diagonal contributions. Provided these benchmarks converge to their ideal adiabatic values, we argue that thermal expectation values of observables can be recovered, in accordance with the eigenstate thermalization hypothesis. For the transverse-field Ising model, we analytically establish that these benchmarks converge polynomially in both the quasi-adiabatic evolution time $T$ and system size. We perform numerical studies on non-integrable systems and find close quantitative agreement for the off-diagonality metrics, along with qualitatively similar behavior in the energy convergence.