Explicit tensor network representation for the ground states of string-net models

Abstract

The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor categories. The construction highlights the importance of the fat lattice to understand these models.

5 pages, pdf figures

References in corpus (12)

• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• String-net condensation: A physical mechanism for topological phases
• Topological orders and Edge excitations in FQH states
• Criticality, the area law, and the computational power of PEPS
• Ground state entanglement and geometric entropy in the Kitaev's model
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Entanglement renormalization and topological order
• Entanglement and topological entropy of the toric code at finite temperature
• Completeness of the classical 2D Ising model and universal quantum computation
• Classical spin models and the quantum stabilizer formalism

Cited by in corpus (112)

• Area laws for the entanglement entropy - a review
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Entanglement Renormalization and Holography
• Tensor networks for complex quantum systems
• PEPS as ground states: degeneracy and topology
• Tensor network states and geometry
• Lecture Notes of Tensor Network Contractions
• Photonic tensor networks produced by a single quantum emitter
• Anyons and matrix product operator algebras
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Diagrammatics for Bose condensation in anyon theories
• Crossing a topological phase transition with a quantum computer
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Projected entangled-pair states can describe chiral topological states
• A hierarchy of topological tensor network states
• Shadows of Anyons
• Mapping topological to conformal field theories through strange correlators
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• A canonical form for Projected Entangled Pair States and applications
• Dualities in one-dimensional quantum lattice models: topological sectors
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Twisted Injectivity in PEPS and the Classification of Quantum Phases
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Chiral projected entangled-pair state with topological order
• Entanglement phases as holographic duals of anyon condensates
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Isometric Tensor Network representation of string-net liquids
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Modular Matrices as Topological Order Parameter by Gauge Symmetry Preserved Tensor Renormalization Approach
• Building Projected Entangled Pair States with a Local Gauge Symmetry
• Sequential generation of projected entangled-pair states
• Characterizing Topological Order with Matrix Product Operators
• Non-Abelian braiding of Fibonacci anyons with a superconducting processor
• Tensor product representation of topological ordered phase: necessary symmetry conditions
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Efficient simulation of Grassmann Tensor Product States
• A critical lattice model for a Haagerup conformal field theory
• Electric-magnetic duality of lattice systems with topological order
• Edge theories in Projected Entangled Pair State models
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Sequential Quantum Circuits as Maps between Gapped Phases
• Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• A generalization of the injectivity condition for Projected Entangled Pair States
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Study of anyon condensation and topological phase transitions from a ${\mathbb{Z}}_4$ topological phase using Projected Entangled Pair States
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Pareto-Efficient Quantum Circuit Simulation Using Tensor Contraction Deferral
• Infinite Matrix Product States for long range SU(N) spin models
• Microscopic description of 2d topological phases, duality and 3d state sums
• Algebraically contractible topological tensor network states
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Topological aspects of the critical three-state Potts model
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Galois conjugated tensor fusion categories and non-unitary CFT
• Mapping between Morita equivalent string-net states with a constant depth quantum circuit
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Local tensor network for strongly correlated projective states
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Condensed Matter Applications of Entanglement Theory
• Mean-field ansatz for topological phases with string tension
• Quantum Yang-Mills theory: an overview of a programme
• Typical Correlation Length of Sequentially Generated Tensor Network States
• Simulating topological tensor networks with Majorana qubits
• Boson condensation and instability in the tensor network representation of string-net states
• Semionic resonating valence bond states
• Constructing topological models by symmetrization: A PEPS study
• Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach
• Signatures of broken parity and time-reversal symmetry in generalized string-net models
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• Determining topological order from infinite projected entangled pair states
• Quantum computational tensor network on string-net condensate
• Numerical detection of symmetry enriched topological phases with space group symmetry
• Quantum Error-Detection at Low Energies
• Transition of a ${\mathbb{Z}}_3$ topologically ordered phase to trivial and critical phases
• Topological Minimally Entangled States via Geometric Measure
• From entanglement renormalisation to the disentanglement of quantum double models
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Tensor-product representations for string-net condensed states
• Galois conjugates of String-net Model
• Projected Entangled Pair States with continuous virtual symmetries
• Locality optimization for parent Hamiltonians of Tensor Networks
• Generation of photonic tensor network states with Circuit QED
• Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• Symmetry topological field theory and non-abelian Kramers-Wannier dualities of generalised Ising models
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Quantum Gauge Networks: A New Kind of Tensor Network
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Strictly local tensor networks for short-range topological insulators
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Quantum Lego and XP Stabilizer Codes
• Virasoro Generators in the Fibonacci Model Tensor Network -- Tackling Finite Size Effects
• Parent Lindbladians for Matrix Product Density Operators
• Les Houches Lecture Notes on Tensor Networks
• Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks
• From gauging to duality in one-dimensional quantum lattice models
• Tensor network states for the description of quantum many-body systems
• Noise-tolerant Detection of $Z_N$ Topological Orders in Quantum Many-body States
• Skeleton of isometric Tensor Network States for Abelian String-Net Models
• Note on searching for critical lattice models as entropy critical points from strange correlator