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

Abstract

The entanglement entropy, $\mathcal{S}$, 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 $\mathcal{S}$ 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 $\mathcal{S}$ across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point $\mathcal{S}$ shows a jump, which is expected to vanish for $Q\to 4^{+}$. This jump is calculated in leading order as $\Delta \mathcal{S}=\ln Q[1-4/Q-2/(Q\ln Q)+\mathcal{O}(1/Q^2)]$.

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