Quantifying Spontaneously Symmetry Breaking of Quantum Many-body Systems

TL;DR

This paper introduces a continuous, group-theoretical measure of symmetry to quantify spontaneous symmetry breaking in quantum many-body systems, linking symmetry reduction directly to the emergence of phenomena like superconductivity and Bose-Einstein condensation.

Contribution

It proposes a novel quantitative measure of symmetry that captures the degree of symmetry breaking and relates it to order parameters in quantum many-body systems.

Findings

Symmetry measure remains unity without emergent phenomena.

Symmetry decreases exponentially with the emergence of order parameters.

The approach maps complex systems into many spin models for analysis.

Abstract

Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry breaking phase. Recently, we have proposed a continuous measure of symmetry of a physical system using group theoretical approach. Within this framework, we study the spontaneous symmetry breaking in the conventional superconductor and Bose-Einstein condensation by showing both the two many body systems can be mapped into the many spin model. Moreover we also formulate the underlying relation between the spontaneous symmetry breaking and the order parameter quantitatively. The degree of symmetry stays unity in the absence of the two emergent phenomena, while decreases exponentially at the appearance of the order parameter which indicates the inextricable relation between the spontaneous symmetry and the order parameter.