Numerical detection of symmetry enriched topological phases with space group symmetry

Understand

Topologically ordered phases of matter, in particular so-called symmetry enriched topological (SET) phases, can exhibit quantum number fractionalization in the presence of global symmetry.

• In Z_2 topologically ordered states in two dimensions, fundamental translations T_x and T_y acting on anyons can either commute or anticommute.
• This property, crystal momentum fractionalization, can be seen in a periodicity of the excited-state spectrum in the Brillouin zone.
• We present a numerical method to detect the presence of this form of symmetry enrichment given a projected entangled pair state (PEPS); we study the minima of spectrum of correlation lengths of the transfer matrix for a cylinder.