Robust symmetry breaking in gapless quantum magnets

TL;DR

This paper proves the existence of spontaneous symmetry breaking in certain gapless quantum systems, using novel mathematical techniques to establish robustness and metastability, advancing the understanding of stable gapless quantum phases.

Contribution

It introduces a rigorous method to demonstrate symmetry breaking and metastability in gapless quantum systems, extending classical concepts to quantum models with nonlocal interactions.

Findings

Established robust ferromagnetism in 2D random-bond Ising models with weak transverse fields.

Provided new proofs of metastability and slow decay of false vacuum states.

Developed a 'many-body WKB' method for analyzing tunneling rates in quantum systems.

Abstract

We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous symmetry breaking of a finite group at some positive temperature. Additionally, the classical model need not be local in space, as long as it satisfies a quantum analogue of the Peierls condition. As an example of our technique, we establish robust ferromagnetism in random-bond Ising models in $d= 2$ dimensions with sufficiently biased random couplings, with weak transverse field. Our mathematical technique is based on establishing quantum bottlenecks, similar to a "many-body WKB" method for evaluating tunneling rates. Using these same methods, we provide new proofs of metastability and the slow decay of the false vacuum, applicable to gapless metastable states. Our work represents a first step towards a rigorous classification of stable gapless quantum phases.