Interplay of SU(2), point group, and translational symmetry for projected entangled pair states: Application to a chiral spin liquid

Abstract

Projected entangled pair states (PEPS) provide exact representations for many non-chiral topologically ordered states whereas their range of applicability to interacting chiral topological phases remains largely unsettled. In this context, the symmetries of the local PEPS tensors are crucial for determining the characteristic topological features of the state. In this article we examine the constraints that arise when different symmetries are imposed simultaneously on the local tensor such as internal SU (2), point group and translation symmetry. We show how the interplay of these symmetries manifests in the entanglement spectrum which is the main diagnostic tool for chiral topological order. We apply our results to a spin liquid PEPS introduced previously as a chiral generalization of the resonating valence bond state. Our findings explain the discrepancies observed between the entanglement spectrum of this state and the expected edge spectrum described by a chiral conformal field theory. Finally, in a certain parameter region where this PEPS possesses an additional U (1) symmetry we are able to resolve these discrepancies and obtain an entanglement spectrum with the expected state countings and conformal weight. arXiv:1805.04531v1 [cond-mat.str-el]

Gradient methods for variational optimization of projected entangled-pair states

“…where the bar denotes complex conjugation of the tensor elements. Note that an explicit breaking of reflection and time-reversal symmetry separately often leads to chiral wavefunctions [40,41]. The interplay between internal symmetries and spatial symmetries leads to non-trivial classes of PEPS wavefunctions [42].…”

Simulating chiral spin liquids with projected entangled-pair states

“…By Gutzwiller projecting two of these Gaussian PEPS, a CSL wavefunction can be constructed, exhibiting an entanglement spectrum with the degeneracy pattern of a chiral conformal field theory. Subsequently, a class of SU(2) invariant PEPS was proposed that exhibits chiral entanglement spectra [58][59][60]. Motivated by the properties of these trial wavefunctions, microscopic CSL Hamiltonians were successfully studied with PEPS, where both SU(2) and spatial symmetries were imposed on the PEPS tensors [61,62]; recently, this approach was even extended to study SU(N ) CSLs [33,63].…”

Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

“…Note that the two dashed lines at low energy correspond, in fact, to a unique chiral mode as it becomes clear by plotting the spectrum in the reduced Brillouin zone [0, π[ (see main text). Note that the spectrum can be "unfolded" and plotted in the full Brillouin zone while still keeping the full SU(2) multiplet structure by using a different gauge for the PEPS that does not preserve the full rotation symmetry of the local tensor [67].…”