Entanglement entropy of the $Q \ge 4$ quantum Potts chain

TL;DR

This paper investigates the entanglement entropy behavior in the ground state of the $Q$-state quantum Potts chain for $Q>4$, revealing a jump at the first-order quantum phase transition point and its dependence on $Q$.

Contribution

The study provides the first calculation of the entanglement entropy jump at a first-order quantum phase transition in the quantum Potts chain for $Q>4$, including its leading order dependence on $Q$.

Findings

Entanglement entropy exhibits a jump at the first-order transition point for $Q>4$.

The jump in entropy vanishes as $Q$ approaches 4 from above.

Leading order expression for the entropy jump is derived as $ riangle { m S}= ext{ln}Q[1-4/Q-2/(Q ext{ln}Q)+{ m O}(1/Q^2)]$.

Abstract

The entanglement entropy, ${\cal S}$, is an indicator of quantum correlations in the ground state of a many body quantum system. At a second-order quantum phase-transition point in one dimension ${\cal S}$ generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the $Q$-state quantum Potts chain for $Q>4$ and calculate ${\cal S}$ across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point ${\cal S}$ shows a jump, which is expected to vanish for $Q \to 4^+$. This jump is calculated in leading order as $\Delta {\cal S}=\ln Q[1-4/Q-2/(Q \ln Q)+{\cal O}(1/Q^2)]$.