Variational and DMRG studies of the Frustrated Antiferromagnetic Heisenberg S=1 Quantum Spin Chain

TL;DR

This paper investigates the phase transitions and incommensurate correlations in a frustrated antiferromagnetic S=1 Heisenberg chain using variational methods and DMRG, identifying key quantum critical points and phase changes.

Contribution

It provides new insights into the quantum phase diagram of the frustrated S=1 Heisenberg chain, including the identification of disorder, Lifshitz, and first-order transition points.

Findings

Disorder point at α_D=0.284(1) marks onset of incommensurate correlations.

Lifshitz point at α_L=0.3725(25) shows degenerate excitation spectrum.

First order transition at α_T=0.7444(6) from AKLT to generalized AKLT phase.

Abstract

We study a frustrated antiferromagnetic isotropic Heisenberg $S=1$ chain using a variational ansatz and the DMRG. At $\alpha_D=0.284(1)$, there is a disorder point of the second kind, marking the onset of incommensurate correlations in the chain. At $\alpha_L=0.3725(25)$ there is a Lifshitz point, at which the excitation spectrum develops a doubly degenerate structure. These points are the quantum remnants of the transition from antiferromagnetic to spiral order in the classical frustrated chain. At $\alpha_T=0.7444(6)$ there is a first order phase transition from an AKLT phase to a next-nearest neighbor generalization of the AKLT model. At the transition, the string order parameter shows a discontinuous jump of 0.085 to 0; the correlation length and the gap are both finite at the transition. The problem of edge states in open frustrated chains is discussed at length.