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

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

2006-12-21

arxiv.org/abs/cond-mat/0612538v2

JSTAT, P05010 (2007).

Physics

Condensed Matter

Statistical Mechanics

19 pages, 2 figures, final version in press at JSTAT

Scientific paper

10.1088/1742-5468/2007/05/P05010

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.

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