Shadows of anyons and the entanglement structure of topological phases

J. Haegeman, V. Zauner, N. Schuch, F. Verstraete
2015 Nature Communications  
The eigenvalue structure of the quantum transfer matrix is known to encode essential information about the elementary excitations. Here we study transfer matrices of quantum states in a topological phase using the tensor network formalism. We demonstrate that topological quantum order requires a particular type of 'symmetry breaking' for the fixed point subspace of the transfer matrix, and relate physical anyon excitations to domain wall excitations at the level of the transfer matrix. A
more » ... ical phase transition to a trivial phase triggers a change in the fixed point subspace to either a larger or smaller symmetry and we explain how this relates to a condensation or confinement of the corresponding anyon sectors. The tensor network formalism enables us to determine the structure of the topological sectors in two-dimensional gapped phases very efficiently, therefore opening novel avenues for studying fundamental open questions related to anyon condensation.
doi:10.1038/ncomms9284 pmid:26440783 pmcid:PMC4600714 fatcat:e4eebqolcjeivn5mt2jgioedta