Are degenerate groundstates induced by spontaneous symmetry breakings in quantum phase transitions?

TL;DR

This paper investigates the role of emergent symmetry in degenerate groundstates during quantum phase transitions, revealing that spontaneous symmetry breaking of a largest common symmetry group explains these phenomena in a quantum spin system.

Contribution

It demonstrates that degenerate groundstates are induced by spontaneous symmetry breaking of the largest common symmetry group in quantum spin systems, linking emergent symmetry to Landau theory.

Findings

Emergent symmetry phenomena are identified in the groundstates of a quantum spin-1/2 plaquette chain.

A covering symmetry group over all emergent symmetries is found to correspond to the largest common symmetry group of the Hamiltonians.

Degenerate groundstates are induced by spontaneous symmetry breaking within this largest common symmetry group.

Abstract

Recently, emergent symmetry is one of fast-growing intriguing issues in many-body systems. Its roles and consequential physics have not been well understood in quantum phase transitions. Emergent symmetry of degenerate groundstates is discussed in possible connection to spontaneous symmetry breaking within the Landau theory. For a clear discussion, a quantum spin-$1/2$ plaquette chain system is shown to have rich emergent symmetry phenomena in its groundstates. A covering symmetry group over all emergent symmetries responsible for degenerate groundstates in the plaquette chain system is found to correspond to a largest common symmetry group of constituent Hamiltonians describing the plaquette system. Consequently, this result suggests that, as a guiding symmetry principle in quantum phase transitions, {\it degenerate groundstates are induced by a spontaneous breaking of symmetries belonging to a largest common symmetry group of continent Hamiltonians describing a given system but can have more symmetries than the largest common symmetry}.