Projected Entangled Pair States with continuous virtual symmetries

Abstract

We study Projected Entangled Pair States (PEPS) with continuous virtual symmetries, i.e., symmetries in the virtual degrees of freedom, through an elementary class of models with SU(2) symmetry. Discrete symmetries of that kind have previously allowed for a comprehensive explanation of topological order in the PEPS formalism. We construct local parent Hamiltonians whose ground space with open boundaries is exactly parametrized by the PEPS wavefunction, and show how the ground state can be made unique by a suitable choice of boundary conditions. We also find that these models exhibit a logarithmic correction to the entanglement entropy and an extensive ground space degeneracy on systems with periodic boundaries, which suggests that they do not describe conventional gapped topological phases, but either critical models or some other exotic phase.

arXiv comment10+14 pages, 7 figures

References in corpus (23)

• An RVB phase in the triangular lattice quantum dimer model
• Classifying quantum phases using Matrix Product States and PEPS
• Topological Order and Conformal Quantum Critical Points
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• PEPS as ground states: degeneracy and topology
• Explicit tensor network representation for the ground states of string-net models
• Projected entangled-pair states can describe chiral topological states
• Realizing non-Abelian statistics
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Chiral projected entangled-pair state with topological order
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
• Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$
• Topological order from quantum loops and nets
• Phase transitions in 3D loop models and the $C{P}^{n-1}$ $\sigma$ model
• A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Coupled Potts models: Self-duality and fixed point structure
• Critical points in coupled Potts models and critical phases in coupled loop models
• Product vacua with boundary states
• Local interactions and non-Abelian quantum loop gases
• Fibonacci topological order from quantum nets
• Universality of coupled Potts models

Cited by in corpus (4)

• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Trimer states with ${\mathbb{Z}}_3$ topological order in Rydberg atom arrays
• The minimal canonical form of a tensor network
• Gapped $Z_2$ spin liquid in the breathing kagome Heisenberg antiferromagnet