Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy

TL;DR

This paper presents a detailed phase diagram of S=1 XXZ chains with uniaxial anisotropy, identifying various phases and transition types through numerical and theoretical analysis.

Contribution

First quantitative phase diagram of the model, accurately locating multiple phase boundaries and transition types using advanced numerical methods.

Findings

Identified six distinct ground state phases including Haldane, large-D, Néel, XY, and ferromagnetic.

Mapped four types of phase transitions: BKT, Gaussian, Ising, and first order.

Precisely determined the critical lines separating different phases.

Abstract

One dimensional S=1 XXZ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization group and finite size scaling method. We thus present the first quantitatively reliable ground state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, N\'{e}el phase, two XY phases and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless type transitions, the Gaussian type transitions, the Ising type transitions and the first order transitions. The location of these critical lines are accurately determined.