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.

arXiv comment29 pages, 14 figures

References in corpus (30)

• Topological Insulators
• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group in the age of matrix product states
• Classification of topological insulators and superconductors in three spatial dimensions
• Periodic table for topological insulators and superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Entanglement spectrum of a topological phase in one dimension
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Classifying quantum phases using Matrix Product States and PEPS
• Criticality, the area law, and the computational power of PEPS
• Entanglement spectrum of topological insulators and superconductors
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Valence Bond Solids for Quantum Computation
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Entanglement spectrum and boundary theories with projected entangled-pair states
• PEPS as ground states: degeneracy and topology
• Fermionic Projected Entangled Pair States
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Characterizing topological order by studying the ground states of an infinite cylinder
• Entanglement in fermionic systems
• Explicit tensor network representation for the ground states of string-net models
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Projected entangled-pair states can describe chiral topological states
• Momentum polarization: an entanglement measure of topological spin and chiral central charge
• Edge theories in Projected Entangled Pair State models

Cited by in corpus (44)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Lecture Notes of Tensor Network Contractions
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Renormalization group constructions of topological quantum liquids and beyond
• Chiral projected entangled-pair state with topological order
• Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Characterizing Topological Order with Matrix Product Operators
• Fermionic projected entangled-pair states and topological phases
• Featureless quantum insulator on the honeycomb lattice
• Holographic Entanglement Renormalization of Topological Insulators
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• Tensor Networks Can Resolve Fermi Surfaces
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Continuum limits of Matrix Product States
• U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
• Exact projected entangled pair ground states with topological Euler invariant
• Projected d-wave superconducting state: a fermionic projected entangled pair state study
• Classification of trivial spin-1 tensor network states on a square lattice
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Variational Tensor Network Operator
• Efficient conversion from fermionic Gaussian states to matrix product states
• Finite-Entanglement Scaling of 2D Metals
• Simulating chiral spin liquids with projected entangled-pair states
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Geometric and computational aspects of chiral topological quantum matter
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Quasi-local Frustration-Free Free Fermions
• Gaussian matrix product states cannot efficiently describe critical systems
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Exact Mappings in Condensed Matter Physics
• Tensor network states for the description of quantum many-body systems