Anyonic entanglement renormalization

Abstract

We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions.

19 pages, 10 figures, v2: extended, updated to match published version

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Cited by in corpus (33)

• Lecture Notes of Tensor Network Contractions
• 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
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Simulation of anyons with tensor network algorithms
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Translation invariance, topology, and protection of criticality in chains of interacting anyons
• Categorical Tensor Network States
• Practical learning method for multi-scale entangled states
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• Anomalies and entanglement renormalization
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• 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
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• Topological lattice field theories from intertwiner dynamics
• 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
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• Classification of topological symmetry sectors on anyon rings
• From entanglement renormalisation to the disentanglement of quantum double models
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• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
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• Symmetry-Protected Local Minima in Infinite DMRG
• Preparing topologically ordered states by Hamiltonian interpolation
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