Gauge Theory Description of Spin Chains and Ladders

TL;DR

This paper maps spin chains and ladders to gauge theories, revealing how the number of legs affects the presence of gapless modes and providing quantitative estimates of spin gaps in ladder systems.

Contribution

It introduces a gauge theory framework for analyzing spin chains and ladders, showing how rung interactions influence gapless modes based on the number of legs.

Findings

Odd-leg ladders retain a gapless mode.

Even-leg ladders become fully gapped.

Spin gap in two-leg ladders is approximately 0.36|J'|.

Abstract

An S=1/2 anti-ferromagnetic spin chain is mapped to the two-flavor massless Schwinger model, which admits a gapless mode. In a spin ladder system rung interactions break the chiral invariance. These systems are solved by bosonization. If the number of legs in a cyclically symmetric ladder system is even, all of the gapless modes of spin chains become gapful. However, if the number of legs is odd, one combination of the gapless modes remains gapless. For a two-leg system we find that the spin gap is about .36 |J'| when the inter-chain Heisenberg coupling J' is small compared with the intra-chain Heisenberg coupling.