Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange

TL;DR

This paper explores the complex phase diagram of a spin-1/2 quantum antiferromagnetic ladder with various interactions, using exact solutions and perturbative methods to identify different phases and symmetries.

Contribution

It provides a comprehensive phase diagram for the model, combining exact solutions and perturbative analysis, highlighting the role of ring exchange and Z_4 symmetry.

Findings

Exact ground states identified for specific parameter regimes

Complete phase diagram constructed including symmetry considerations

Perturbative analysis reveals phases at strong ring-exchange coupling

Abstract

We investigate the phase diagram of a generalized spin-1/2 quantum antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange interactions. We consider the exactly soluble models associated with the problem, obtain the exact ground states which exist for certain parameter regimes, and apply a variety of perturbative techniques in the regime of strong ring-exchange coupling. By combining these approaches with considerations related to the discrete Z_4 symmetry of the model, we present the complete phase diagram.