Finding the Generalized Gibbs Ensemble in the Real Space Entanglement Spectra of (2+1)-dimensional Chiral Topological Systems

The numerical calculation of entanglement spectra (ES) has become a useful way to diagnose topological properties of interesting many-body ground states. For (2+1)D quantum Hall states a correspondence between the low-lying levels of the ES across a given bipartition and of the physical spectrum of the edge states along the same cut was observed in Ref. [1]. When the ES of a chiral topological state is computed at a (finite) real space entanglement cut, however, we posit that additional physics should be visible in the splitting of the degeneracies of the low-lying energy levels arising from the presence of higher-order conserved quantities (irrelevant in the renormalization group sense) in the generalized Gibbs ensemble (GGE) associated to the theory on the edge. We analyzed the real space ES obtained in several previous numerical studies of (2+1)D chiral spin liquids with edges hosting (1+1)D conformal field theories possessing SU(2)-level-1 and SU(2)-level-2 symmetry. We fitted the splittings in these ES with sets of (irrelevant) conserved quantities and find that for the most part, we confirm their correspondence with the GGE picture outlined above.

[1] H. Li and F. D. M. Haldane, Phys. Rev. Lett. 101, 010504 (2008).