Mutual information and spontaneous symmetry breaking

TL;DR

This paper demonstrates that symmetry-breaking ground states in quantum many-body systems exhibit minimal quantum mutual information between distant regions, indicating they are the most classical states, supported by general proof and specific model verification.

Contribution

The paper proves that symmetry-breaking ground states have minimal quantum mutual information among all quantum ground states, using a general approach and specific model analysis.

Findings

Symmetry-breaking states have vanishing mutual information at large distances.

The proof uses 2-Rényi entanglement entropy and quasi-adiabatic continuation.

Verification in the 1D quantum XY model confirms the general result.

Abstract

We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g. at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly non trivial. We prove this result in general, by considering the quantum mutual information based on the $2-$R\'enyi entanglement entropy and using a locality result stemming from quasi-adiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum $XY$ model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy.