Critical Properties of Spin-1 Antiferromagnetic Heisenberg Chains with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy

TL;DR

This paper investigates the phase diagram and critical properties of one-dimensional S=1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial anisotropy using numerical and theoretical methods.

Contribution

It provides a detailed numerical analysis of the ground states and critical parameters, including phase boundaries and exponents, for models with bond alternation and anisotropy.

Findings

Identification of ground states: Haldane, large-D, and dimer states.

Calculation of the phase diagram using twisted boundary conditions.

Determination of the dependence of Luttinger liquid parameters and critical exponents on model parameters.

Abstract

One dimensional S=1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for $D\geq 0$. The ground states of this model contain the Haldane state, large-D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and $\delta$-dependence of the Luttinger liquid paraments K and the critical exponent $\nu$ of the energy gap.