Simulation of anyons with tensor network algorithms

Abstract

Interacting systems of anyons pose a unique challenge to condensed matter simulations due to their non-trivial exchange statistics. These systems are of great interest as they have the potential for robust universal quantum computation, but numerical tools for studying them are as yet limited. We show how existing tensor network algorithms may be adapted for use with systems of anyons, and demonstrate this process for the 1-D Multi-scale Entanglement Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of interacting Fibonacci anyons, computing their scaling dimensions and local scaling operators. The scaling dimensions obtained are seen to be in agreement with conformal field theory. The techniques developed are applicable to any tensor network algorithm, and the ability to adapt these ansaetze for use on anyonic systems opens the door for numerical simulation of large systems of free and interacting anyons in one and two dimensions.

Fixed typos, matches published version. 16 pages, 21 figures, 4 tables, RevTeX 4-1. For a related work, see arXiv:1006.2478

References in corpus (29)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Entanglement renormalization
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Interacting anyons in topological quantum liquids: The golden chain
• Algorithms for entanglement renormalization
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Cluster algorithms for general-S quantum spin systems
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Fermionic Projected Entangled Pair States
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• A short introduction to Fibonacci anyon models
• Entanglement renormalization, scale invariance, and quantum criticality
• Entanglement renormalization in two spatial dimensions
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
• A Density Matrix Algorithm for 3D Classical Models
• Unitary circuits for strongly correlated fermions
• Quantum MERA Channels
• Collective states of interacting Fibonacci anyons
• The Density Matrix Renormalization Group Method applied to Interaction Round a Face Hamiltonians
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Anyonic entanglement renormalization

Cited by in corpus (47)

• Tensor networks for complex quantum systems
• Tensor network decompositions in the presence of a global symmetry
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Lecture Notes of Tensor Network Contractions
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Faster identification of optimal contraction sequences for tensor networks
• Dualities in one-dimensional quantum lattice models: topological sectors
• A critical lattice model for a Haagerup conformal field theory
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Quantum group spin nets: refinement limit and relation to spin foams
• Translation invariance, topology, and protection of criticality in chains of interacting anyons
• Practical learning method for multi-scale entangled states
• Categorical Tensor Network States
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Anomalies and entanglement renormalization
• Symmetry protected entanglement renormalization
• Matrix product states for anyonic systems and efficient simulation of dynamics
• DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains
• Mean-field ansatz for topological phases with string tension
• Quantum phases of a chain of strongly interacting anyons
• Topological lattice field theories from intertwiner dynamics
• Measures of entanglement in non-Abelian anyonic systems
• Finite Density Matrix Renormalisation Group Algorithm for Anyonic Systems
• Continuum limits of homogeneous binary trees and the Thompson group
• Simulation of braiding anyons using Matrix Product States
• Anyons in Geometric Models of Matter
• MERA as a holographic strange correlator
• Numerical simulation of non-abelian anyons
• From entanglement renormalisation to the disentanglement of quantum double models
• Classification of topological symmetry sectors on anyon rings
• Matrix Product State representation for Slater Determinants and Configuration Interaction States
• Matrix product approximations to conformal field theories
• Many-body Lattice Wavefunctions From Conformal Blocks
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Simulation of Quantum Many-Body Systems on Amazon Cloud
• Matrix product states for $su(2)$ invariant quantum spin chains
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Collective states of interacting $D(D_3)$ non-Abelian anyons
• Lattice models from CFT on surfaces with holes I: Torus partition function via two lattice cells
• Symmetry-Protected Local Minima in Infinite DMRG
• Preparing topologically ordered states by Hamiltonian interpolation
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling