The spin-1 ladder : A bosonization study

TL;DR

This paper develops a bosonic field theory for a spin-1 ladder system, revealing how interchain coupling influences the spin gap and exploring potential incommensurate phases.

Contribution

It provides a novel bosonization approach for coupled spin-1 chains, including detailed analysis of the effects of interchain coupling on the spin gap.

Findings

Spin gap decreases linearly with interchain coupling.

Spin-1 ladder approximated by three decoupled sine-Gordon models.

Discussion of possible incommensurate phase in zigzag chains.

Abstract

We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two-frequency sine-Gordon models. We then predict that, starting with decoupled chains, the spin gap decreases linearly with interchain coupling, both in the ferromagnetic and antiferromagnetic directions. Finally, we discuss the possibility of an incommensurate phase in the spin-1 zigzag chain.