Matrix product states for anyonic systems and efficient simulation of dynamics

TL;DR

This paper extends matrix product states to simulate topologically ordered anyonic systems, enabling efficient study of their ground states and dynamics, including transport properties, through an adapted TEBD algorithm.

Contribution

It introduces an anyonic MPS formalism with charge-conserving tensors and adapts TEBD for simulating anyonic system dynamics.

Findings

Successfully simulated ground states of Ising and Fibonacci anyons.

Demonstrated real-time dynamics of an anyonic Hubbard-like model.

Provided insights into anyon transport properties.

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.