Mixed-spin cluster expansion for a quasi-one-dimensional Haldane system

TL;DR

This paper introduces a new mixed-spin cluster expansion method to analyze a quasi-one-dimensional Haldane system, enabling precise phase diagram determination and direct study of the Haldane phase.

Contribution

The paper develops a novel mixed-spin cluster expansion technique that directly addresses the Haldane phase in quasi-one-dimensional systems, surpassing standard methods.

Findings

Successfully mapped the s=1 antiferromagnetic model to a mixed-spin model

Precisely determined the phase diagram of the system

Identified the competition among Haldane, dimer, and magnetic phases

Abstract

We present a novel mixed-spin cluster expansion method for a quasi-one-dimensional Haldane system with bond alternation. By mapping the s=1 antiferromagnetic spin model on square and cubic lattices to the equivalent mixed-spin model, we study the competition among the Haldane, the dimer and the magnetically ordered phases. The mixed-spin cluster expansion proposed here allows us to directly deal with the Haldane phase, which may not be reached by standard series expansion methods. The phase diagram is determined rather precisely by making use of an additional symmetry property in the effective mixed-spin model introduced.