Matrix product states for anyonic systems and efficient simulation of dynamics

Abstract

Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved topological charges and collectively carry non-local degrees of freedom. In this paper we extend the formalism of MPS to lattice systems of anyons. The anyonic MPS is constructed from tensors that explicitly conserve topological charge. We describe how to adapt the time-evolving block decimation (TEBD) algorithm to the anyonic MPS in order to simulate dynamics under a local and charge-conserving Hamiltonian. To demonstrate the effectiveness of anyonic TEBD algorithm, we used it to simulate (i) the ground state (using imaginary time evolution) of an infinite 1D critical system of (a) Ising anyons and (b) Fibonacci anyons both of which are well studied, and (ii) the real time dynamics of an anyonic Hubbard-like model of a single Ising anyon hopping on a ladder geometry with an anyonic flux threading each island of the ladder. Our results pertaining to (ii) give insight into the transport properties of anyons. The anyonic MPS formalism can be readily adapted to study systems with conserved symmetry charges, as this is equivalent to a specialization of the more general anyonic case.

18 pages, 15 figues

References in corpus (13)

• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• A class of quantum many-body states that can be efficiently simulated
• Interacting anyons in topological quantum liquids: The golden chain
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• A short introduction to Fibonacci anyon models
• Anyonic quantum spin chains: Spin-1 generalizations and topological stability
• Simulation of anyons with tensor network algorithms
• Anyonic entanglement renormalization
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• One-dimensional itinerant interacting non-Abelian anyons
• Statistical dynamics of a non-Abelian anyonic quantum walk
• Monte Carlo Simulations of Interacting Anyon Chains

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• Simulation of braiding anyons using Matrix Product States
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• Numerical simulation of non-abelian anyons
• Matrix product approximations to conformal field theories
• Phase transitions on a ladder of braided non-Abelian anyons
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Mode folding in systems with local interaction: unitary and non-unitary transformations using tensor states
• Symmetry-Protected Local Minima in Infinite DMRG
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Les Houches Lecture Notes on Tensor Networks
• Chiral Edge States Emerging on Anyon-Net
• Categorical Quantum Volume Operator
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling