Numerical simulation of non-abelian anyons

Abstract

Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general abelian and non-abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons and Ising anyons. Additionally, we simulate non-equilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times - indicating thermalization.

39 pages, 19 figures

References in corpus (19)

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• The distribution of the ratio of consecutive level spacings in random matrix ensembles
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• Collective states of interacting Fibonacci anyons
• Simulation of anyons with tensor network algorithms
• Anyonic entanglement renormalization
• Anyonic Entanglement and Topological Entanglement Entropy
• One-dimensional itinerant interacting non-Abelian anyons
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices

Cited by in corpus (3)

• Detection of anyon braiding through pump-probe spectroscopy
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling