Mixed-order transition in the antiferromagnetic quantum Ising chain in a field

TL;DR

This paper investigates the phase transition in the antiferromagnetic quantum Ising chain under a longitudinal field, revealing a mixed-order transition characterized by divergent correlation length and discontinuous correlations.

Contribution

It demonstrates that the phase transition becomes mixed-order for finite longitudinal field, combining features of both first- and second-order transitions, using DMRG and renormalization group methods.

Findings

Divergent correlation length at the transition point with TIM exponents

Discontinuous bulk correlation function at the transition

Discontinuous derivative of end-to-end correlation function

Abstract

The antiferromagnetic quantum Ising chain has a quantum critical point which belongs to the universality class of the transverse Ising model (TIM). When a longitudinal field ($h$) is switched on, the phase transition is preserved, which turns to first-order for $h/\Gamma \to \infty$, $\Gamma$ being the strength of the transverse field. Here we will re-examine the critical properties along the phase transition line. During a quantum block renormalization group calculation, the TIM fixed point for $h/\Gamma>0$ is found to be unstable. Using DMRG techniques, we calculated the entanglement entropy and the spin-spin correlation function, both of which signaled a divergent correlation length at the transition point with the TIM exponents. At the same time, the bulk correlation function has a jump and the end-to-end correlation function has a discontinuous derivative at the transition point. Consequently for finite $h/\Gamma$ the transition is of mixed-order.