Statistical mechanics of the Cluster-Ising model

TL;DR

This paper analyzes a quantum spin model combining cluster and Ising interactions, revealing a phase transition with unique entanglement properties and a critical point beyond the Ising universality class.

Contribution

It provides a detailed analysis of the phase diagram, entanglement, and criticality of a combined cluster-Ising model, highlighting novel quantum phase transition features.

Findings

Quantum phase transition between Ising and cluster phases.

Vanishing two-spin entanglement in both phases.

Maximal multipartite entanglement in the cluster phase.

Abstract

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like anti-ferromagnetic interaction. We compute free energy, spin correlation functions and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Neverthless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.