Quantum criticality in dimerised anisotropic spin-1 chains

TL;DR

This paper investigates how dimerisation affects the quantum phase transitions in spin-1 XXZ chains with single-ion anisotropy, revealing a critical dimerisation threshold and identifying Ising and tricritical Ising universality classes.

Contribution

It demonstrates the survival of the Haldane phase up to a critical dimerisation and uncovers a continuous Ising quantum phase transition with specific critical exponents.

Findings

Haldane phase persists up to a critical dimerisation

Dimerisation induces a continuous Ising transition with central charge 1/2

Critical exponents match Ising and tricritical Ising universality classes

Abstract

Applying the (infinite) density-matrix renormalisation group technique, we explore the effect of an explicit dimerisation on the ground-state phase diagram of the spin-1 $XXZ$ chain with single-ion anisotropy $D$. We demonstrate that the Haldane phase between large-$D$ and antiferromagnetic phases survives up to a critical dimerisation only. As a further new characteristic the dimerisation induces a direct continuous Ising quantum phase transition between the large-$D$ and antiferromagnetic phases with central charge $c=1/2$, which terminates at a critical end-point where $c=7/10$. Calculating the critical exponents of the order parameter, neutral gap and spin-spin-correlation function, we find $\beta=1/8$ (1/24), $\nu=1$ (5/9), and $\eta=1/4$ (3/20), respectively, which proves the Ising (tricritical Ising) universality class in accordance with field-theoretical predictions.