Fermionic projected entangled-pair states and topological phases

Abstract

We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic topological order. The tensor network states allow us to relate physical properties of the topological phases to the underlying algebraic data. We illustrate this by calculating defect properties and modular matrices of supercohomology phases. Our formalism also captures Majorana defects as we show explicitly for a class of ${\mathbb{Z}}_2$ symmetry-protected and intrinsic topological phases. The tensor networks states presented here are well-suited for numerical applications and hence open up new possibilities for studying interacting fermionic topological phases.

Published version

References in corpus (40)

• 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 phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• PEPS as ground states: degeneracy and topology
• Fermionic Projected Entangled Pair States
• Topological Defects on the Lattice I: The Ising model
• Interacting topological phases and modular invariance
• Fermionic SPT phases in higher dimensions and bosonization
• Spin TQFTs and fermionic phases of matter
• Fermionic multi-scale entanglement renormalization ansatz
• Anyons and matrix product operator algebras
• Interaction effect on topological classification of superconductors in two dimensions
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• Gauging quantum states: from global to local symmetries in many-body systems
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Projected entangled-pair states can describe chiral topological states
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Twisted Injectivity in PEPS and the Classification of Quantum Phases
• A classification of 2D fermionic and bosonic topological orders
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Lattice Model for Fermionic Toric Code
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• A generalization of the injectivity condition for Projected Entangled Pair States
• Spin Topological Field Theory and Fermionic Matrix Product States
• Fermionic topological quantum states as tensor networks
• Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states
• Fermionic Matrix Product Operators and Topological Phases of Matter

Cited by in corpus (43)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Tensor networks for complex quantum systems
• Lecture Notes of Tensor Network Contractions
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Mapping topological to conformal field theories through strange correlators
• Dualities in one-dimensional quantum lattice models: topological sectors
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Towards a mathematical formalism for classifying phases of matter
• Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Fermionic tensor network methods
• On the stability of topological order in tensor network states
• Global anomaly detection in two-dimensional symmetry-protected topological phases
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• On tensor network representations of the (3+1)d toric code
• Filling constraints on fermionic topological order in zero magnetic field
• Competing orders in the honeycomb lattice $t$-$J$ model
• A unified diagrammatic approach to topological fixed point models
• On ${\mathbb{Z}}_2$-indices for ground states of fermionic chains
• A tensor network approach to 2D bosonization
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Supersymmetric boundaries of one-dimensional phases of fermions beyond symmetry-protected topological states
• Fermionic Isometric Tensor Network States in Two Dimensions
• Intermediate symmetric construction of transformation between anyon and Gentile statistics
• Topological dualities via tensor networks
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Towards topological fixed-point models beyond gappable boundaries
• Fermionic tensor network contraction for arbitrary geometries
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Finite-Entanglement Scaling of 2D Metals
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Competing pair density wave orders in the square lattice $t$-$J$ model
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• Grassmann tensor networks
• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods
• A minimal tensor network beyond free fermions