Generalized nonlinear sigma model approach to alternating spin chains and ladders

TL;DR

This paper extends the nonlinear sigma model to include ferromagnetic bonds in quantum spin chains, successfully describing phase crossovers and matching DMRG data.

Contribution

It introduces a generalized formalism for nonlinear sigma models to handle ferromagnetic bonds and complex phase transitions in spin chains and ladders.

Findings

Successfully reproduces crossover between decoupled dimers and Haldane phase.

Shows good agreement between analytical results and DMRG data.

Extends the sigma model approach to more complex spin systems.

Abstract

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Neel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-leg spin ladder and the Haldane phase. Here again we show that there is good agreement between DMRG data and our analytical results.