APS -APS March Meeting 2017 - Event - Symmetry protected valence bond solid states and strange correlator

摘要

We describe symmetry-protected topological (SPT) propertiesof quantum antiferromagnets using an effective field theoryof nonlinear sigma models with topological Berry phase terms.We mainly focus on valence-bond-solid states on a two-dimensional square lattice,which has a spatially uniform ground statewhen the spin quantum number $S$ is an even integer.By representing the ground state wave functionalthrough a path integral, SPT properties appear in temporal surface termof a field theory defined in a spacewhose dimensionality is reduced by one.This representation allows us to conclude thatthe ground state can be an SPT state for $S=2imes{m odd}$ integerwhile topologically trivial for $S=2imes{m even}$ integer.We also show that this temporal surface termin the ground state wave functional is equivalent to strange correlator,which is proposed as an indicator of SPT phases.