Phase diagram of S=1 XXZ chain with next-nearest neighbor interaction

TL;DR

This paper investigates the phase diagram of the S=1 XXZ chain with next-nearest-neighbor interactions using numerical and analytical methods, identifying phase boundaries and universality classes.

Contribution

It provides a comprehensive numerical and analytical analysis of the phase diagram, including the effects of next-nearest-neighbor interactions and anisotropy.

Findings

Identified phase boundaries among XY, Haldane, ferromagnetic, and Néel phases.

Confirmed the universality class of phase transitions.

Mapped the model onto the non-linear sigma model for further analysis.

Abstract

The one dimensional S=1 XXZ model with next-nearest-neighbor interaction $\alpha$ and Ising-type anisotropy $\Delta$ is studied by using a numerical diagonalization technique. We discuss the ground state phase diagram of this model numerically by the twisted-boundary-condition level spectroscopy method and the phenomenological renormalization group method, and analytically by the spin wave theory. We determine the phase boundaries among the XY phase, the Haldane phase, the ferromagnetic phase and the N\'{e}el phase, and then we confirm the universality class. Moreover, we map this model onto the non-linear $\sigma$ model and analyze the phase diagram in the $\alpha$ $\ll$ -1 and $\Delta$ $\sim$ 1 region by using the renormalization group method.