$\mu$-Symmetry breaking: an algebraic approach to finding mean fields of quantum many-body systems

TL;DR

This paper introduces a systematic algebraic method for identifying mean fields in quantum many-body systems experiencing spontaneous symmetry breaking, utilizing Lie algebra and dynamical symmetry concepts.

Contribution

It proposes the novel concept of $$-symmetry breaking and demonstrates how it enables systematic analysis of effective Lagrangians and topological excitations.

Findings

Quadratic parts of effective Lagrangians can be block-diagonalized.

Homotopy groups of topological excitations can be systematically calculated.

The method provides a structured approach to mean field identification in symmetry-broken phases.

Abstract

One of the most fundamental problems in quantum many-body systems is the identification of a mean field in spontaneous symmetry breaking which is usually made in a heuristic manner. We propose a systematic method of finding a mean field based on the Lie algebra and the dynamical symmetry by introducing a class of symmetry broken phases which we call $\mu$-symmetry breaking. We show that for $\mu$-symmetry breaking the quadratic part of an effective Lagrangian of Nambu-Goldstone modes can be block-diagonalized and that homotopy groups of topological excitations can be calculated systematically.