Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain

TL;DR

This paper investigates the phase diagram of a bilinear-biquadratic S=1 zig-zag chain, revealing a novel trimerized phase with an energy gap near known phases, using advanced numerical methods.

Contribution

It introduces the discovery of a trimerized phase in the S=1 zig-zag chain, expanding understanding of its quantum phase diagram.

Findings

Identification of a trimerized phase with a nonzero energy gap

Analysis of order parameters and correlation functions

Connection of numerical results to field theoretical predictions

Abstract

Recent theoretical studies raised the possibility of a realization of spin nematic states in the S=1 triangular lattice compound NiGa_2S_4. We study the bilinear-biquadratic spin 1 chain in a zig-zag geometry by means of the density matrix renormalization group method and exact diagonalization. We present the phase diagram focusing on antiferromagnetic interactions. Adjacent to the known Haldane-double Haldane and the extended critical phase with dominant spin nematic correlations we find a trimerized phase with a nonvanishing energy gap. We discuss results for different order parameters, energy gaps, correlation functions, and the central charge, and make connection to field theoretical predictions for the phase diagram.