Fate of the cluster state on the square lattice in a magnetic field

TL;DR

This paper investigates the stability of the two-dimensional square lattice cluster state under external magnetic fields, revealing a phase diagram with first-order transitions, critical points, and a self-dual line, using advanced computational methods.

Contribution

It introduces a comprehensive analysis of the cluster state's robustness in a magnetic field, highlighting the existence of a self-dual line and detailed phase transition characteristics.

Findings

First-order phase transition line identified

Critical end points located in the phase diagram

Self-dual line exists on any lattice topology

Abstract

The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology.