Flux period, spin gap, and pairing in the one-dimensional t-J-J'-model

TL;DR

This paper explores the relationship between spin gaps and flux periodicity in the one-dimensional t-J-J' model, proposing a conjecture linking spin gaps, flux periodicity, and symmetry breaking in Luttinger liquids.

Contribution

It demonstrates the connection between spin gaps and flux periodicity using wavefunction factorization and conjectures a universal relation in SU(2)-invariant Luttinger liquids.

Findings

Spin gaps imply hc/2e flux periodicity in the model.

Gapped spin-1/2 chains break translational symmetry.

Conjecture: all spin-gapped SU(2)-invariant Luttinger liquids exhibit hc/2e flux periodicity.

Abstract

Using the factorization of the wavefunction in the t-J-J'-model at small exchange couplings, we demonstrate the connection between the existence of a spin gap and an hc/2e flux periodicity of the ground state energy. We conjecture that all spin-gapped SU(2)-invariant Luttinger liquids have hc/2e flux periodicity, and that this is connected to the fact that a gapped spin-1/2 chain always breaks translational symmetry by doubling the unit cell.