Complexity of thermal states in quantum spin chains

TL;DR

This paper investigates the complexity and quantum correlations of thermal states in various quantum spin chains, revealing saturation behaviors and divergence patterns, and introduces an efficient method for entropy computation.

Contribution

It establishes a general relation between quantum mutual information and entanglement entropy, and proposes a quasi-exact computational method for thermalized XY spin chains.

Findings

Mutual information and entanglement entropy saturate with system size.

Logarithmic divergence of entropy in critical cases with inverse temperature.

Uniform bounds on entropy in non-critical cases.

Abstract

We study quantum correlations and complexity of simulation, characterized by quantum mutual information and entanglement entropy in operator space respectively, for thermal states in critical, non-critical and quantum chaotic spin chains. A simple general relation between the two quantities is proposed. We show that in all cases mutual information and entanglement entropy saturate with the system size, whereas as a function of the inverse temperature, we find logarithmic divergences for critical cases and uniform bounds in non-critical cases. A simple efficient quasi-exact method for computation of arbitrary entropy related quantities in thermalized XY spin chains is proposed.