Phase Diagram of S=1 Bond-Alternating XXZ Chains Reflecting the Hidden Z_2\times Z_2 Symmetry

TL;DR

This paper maps the phase diagram of the spin-1 bond-alternating XXZ chain, revealing various quantum phases and phase transitions, and interprets critical behaviors through hidden symmetries and universality classes.

Contribution

It provides a detailed numerical analysis of the phase diagram, identifying phase boundaries and universality classes, and links the critical properties to hidden Z_2×Z_2 symmetry.

Findings

Identified multiple quantum phases: ferromagnetic, XY, Haldane, dimer, N9el.

Classified phase transitions: BKT, Gaussian, Ising types.

Connected critical behaviors to hidden Z_292Z_2 symmetry.

Abstract

The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the N\'eel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times Z_2 symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-N\'eel and dimer-N\'eel). We determine the phase boundary and universality class using the recent developed techniques by the authors.