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 $\Delta \mathcal{S}=\ln Q[1-4/Q-2/(Q\ln Q)+\mathcal{O}(1/Q^2)]$.

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement negativity in quantum field theory
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Evolution of entanglement after a local quench
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Solution of the fermionic entanglement problem with interface defects
• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Entanglement entropy of aperiodic quantum spin chains
• Increasing of entanglement entropy from pure to random quantum critical chains
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Entanglement entropy of the random spin-1 Heisenberg chain