Quasi-Adiabatic Continuation in Gapped Spin and Fermion Systems: Goldstone's Theorem and Flux Periodicity

TL;DR

This paper uses quasi-adiabatic continuation to analyze gapped spin and fermion systems, deriving a form of Goldstone's theorem and demonstrating flux insertion effects with minimal energy change.

Contribution

It introduces a general form of Goldstone's theorem for gapped nonrelativistic systems and shows flux insertion results in fermionic systems with a spin gap.

Findings

Goldstone's theorem extended to gapped nonrelativistic systems

Flux insertion causes exponentially small energy change in spin-gapped fermionic systems

Applicable to superconductors and valence bond states

Abstract

We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonrelativistic systems with continuous symmetries. We then show that for a fermionic system with a spin gap, it is possible to insert $\pi$-flux into a cylinder with only exponentially small change in the energy of the system, a scenario which covers several physically interesting cases such as an s-wave superconductor or a resonating valence bond state.