Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain

TL;DR

This paper investigates the Gaussian topological phase transition in a quantum spin-1 chain using tangential finite-size scaling, accurately locating the critical line and analyzing critical exponents.

Contribution

It introduces a tangential finite-size scaling method to precisely identify the Gaussian critical line and analyze critical exponents in the spin-1 XXZ model.

Findings

Successfully locates the Gaussian critical line.

Probes varying correlation length critical exponents.

Highlights differences from standard Ising-like scaling.

Abstract

Scaling aspects of Gaussian topological phase-transitions in quantum spin chains are investigated using the prototypical one-dimensional spin-1 XXZ Heisenberg model with uniaxial single-ion anisotropy $D$. This model presents a critical line separating the gaped Haldane and large-$D$ phases, with the relevant energy gap closing at the transition point. We show that a proper tangential finite-size scaling analysis is able to accurately locate the Gaussian critical line and to probe the continuously varying set of correlation length critical exponents. The specific features of the tangential scaling are highlighted in contrast with the standard scaling holding in the Ising-like transition between the gapless AF-N\'eel and gaped Haldane phases. Our results are compared with field-theoretic predictions and available high-accuracy data for specific points along the Gaussian line.