Anyon dynamics with matrix product states

Ian McCulloch^1*, Jesse Osborne¹

¹Physics, University of Queensland, Queensland, Australia

* Presenter:Ian McCulloch, email:ianmcc@physics.uq.edu.au

Matrix Product States (MPS) are a computational tool for variational wavefunctions and real-time evolution that is useful for probing ground-states and excitations in a wide variety of settings. Here we show some recent work to examine the dynamics of anyons on 2D cylinders using real-time evolution. By constructing excitations and moving them around the lattice, we can determine explicitly the fractional quantum statistics of anyon excitations in the Toric Code and Kitaev models of topological ordered states, and we are also able to use real-time dynamics of excitations to move between different ground-state degeneracy sectors. This povides a tool that may be useful to characterise topologically ordered states in more difficult cases, beyond exactly solvable models.

Keywords: topological order, non-equilibrium system, anyons, tensor network, manybody physics