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

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.

12 pages, 9 figures

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• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Subsystem symmetry enriched topological order in three dimensions
• Tensor Networks contraction and the Belief Propagation algorithm
• Gauging tensor networks with belief propagation
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Duality viewpoint of criticality
• The minimal canonical form of a tensor network
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Linked Cluster Expansions via Hypergraph Decompositions
• Quantum phase transitions in the $K$-layer Ising toric code
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Scalable projected entangled-pair state representation of random quantum circuit states
• Phases and Quantum Phase Transitions in Anisotropic Antiferromagnetic Kitaev-Heisenberg-$\Gamma$ magnet