Long range order and symmetry breaking in Projected Entangled Pair State models

Abstract

Projected Entangled Pair States (PEPS) provide a framework for the construction of models where a single tensor gives rise to both Hamiltonian and ground state wavefunction on the same footing. A key problem is to characterize the behavior which emerges in the system in terms of the properties of the tensor, and thus of the Hamiltonian. In this paper, we consider PEPS models with ${\mathbb{Z}}_2$ on-site symmetry and study the occurence of long-range order and spontaneous symmetry breaking. We show how long-range order is connected to a degeneracy in the spectrum of the PEPS transfer operator, and how the latter gives rise to spontaneous symmetry breaking under perturbations. We provide a succinct characterization of the symmetry broken states in terms of the PEPS tensor, and find that using the symmetry broken states we can derive a local entanglement Hamiltonian, thereby restoring locality of the entanglement Hamiltonian for all gapped phases.

v2: 9 pages, 4 figures. Significantly extended version, accepted at Phys. Rev. B

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• Entanglement phases as holographic duals of anyon condensates
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Entanglement Hamiltonians for chiral fermions with zero modes
• Entanglement Hamiltonians and entropy in 1+1D chiral fermion systems
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Holographic encoding of universality in corner spectra
• Classifying parafermionic gapped phases using matrix product states
• ${\mathbb{Z}}_N$ symmetry breaking in Projected Entangled Pair State models