Classical nature of ordered phases: origin of spontaneous symmetry breaking

TL;DR

This paper proposes that the most classical ground states in quantum systems, which exhibit maximum symmetry breaking, are characterized by unique local convertibility, minimal quantum correlations, and the ability to be derived from all other states via local operations.

Contribution

It establishes a quantitative link between maximal symmetry breaking and classicality in quantum ground states, highlighting their unique entanglement and correlation properties.

Findings

Maximally symmetry breaking ground states are locally convertible from all others.

These states minimize bipartite quantum entanglement and quantum discord.

They are the only states with asymptotically vanishing pairwise quantum correlations.

Abstract

We investigate the nature of spontaneous symmetry breaking in complex quantum systems by conjecturing that the maximally symmetry breaking quantum ground states are the most classical ones corresponding to an ordered phase. We make this argument quantitatively precise by showing that the ground states which realize the maximum breaking of the Hamiltonian symmetries are the only ones that: I) are always locally convertible, i.e. can be obtained from all other ground states by local operations and classical communication, while the reverse is never possible; II) minimize the monogamy inequality for bipartite entanglement; III) minimize quantum correlations, as measured by the quantum discord, for all pairs of dynamical variables and are the only ground states for which the pairwise quantum correlations vanish asymptotically with the intra-pair distance.