Symmetries and boundary theories for chiral Projected Entangled Pair States

Abstract

We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled-pair states (PEPS). They are ground states of two different kinds of Hamiltonians. The first one, ${\mathcal{H}}_{\mathrm{ff}}$, is local, frustration-free, and gapless. It can be interpreted as describing a quantum phase transition between different topological phases. The second one, ${\mathcal{H}}_{\mathrm{fb}}$ is gapped, and has hopping terms scaling as $1/r^3$ with the distance $r$. The gap is robust against local perturbations, which allows us to define a Chern number for the PEPS. As for (non-chiral) topological PEPS, the non-trivial topological properties can be traced down to the existence of a symmetry in the virtual modes that are used to build the state. Based on that symmetry, we construct string-like operators acting on the virtual modes that can be continuously deformed without changing the state. On the torus, the symmetry implies that the ground state space of the local parent Hamiltonian is two-fold degenerate. By adding a string wrapping around the torus one can change one of the ground states into the other. We use the special properties of PEPS to build the boundary theory and show how the symmetry results in the appearance of chiral modes, and a universal correction to the area law for the zero Rényi entropy.

29 pages, 14 figures

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Cited by in corpus (9)

• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Chiral projected entangled-pair state with topological order
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Fermionic projected entangled-pair states and topological phases
• Geometric and computational aspects of chiral topological quantum matter
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Exact Mappings in Condensed Matter Physics