Quantized Berry phases for a local characterization of spin liquids in frustrated spinsystems

Abstract

Recently, by using quantized Berry phases, a prescription for a local characterization ofgapped topological insulators has been given (Hatsugai 2006 Preprint cond-mat/0603230).It requires that the ground state is gapped and is invariant under some anti-unitaryoperation. A spin liquid which is realized as a unique ground state of the Heisenberg spinsystem with frustrations is a typical target system, since pairwise exchange couplings arealways time-reversal invariants even with frustrations.As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by acontinuous SU(2) twist only at a specific link and define the Berry connection by the derivative. Then theBerry phase evaluated by the entire many-spin wavefunction is used to define the localtopological order parameter at the link. We numerically apply this scheme for several spinliquids and show its physical validity. For example, it implies that the Haldane phase of theS = 1 chains is characterizedby uniform π quantized Berry phases.