Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems

Abstract

Recently by using quantized Berry phases, a prescription for a local characterization of gapped topological insulators is given. One requires the ground state is gapped and is invariant under some anti-unitary operation. A spin liquid which is realized as a unique ground state of the Heisenberg spin system with frustrations is a typical target system, since pairwise exchange couplings are always time-reversal invariants even with frustrations. As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by a continuous SU(2) twist only at a specific link and define the Berry connection by the derivative. Then the Berry phase evaluated by the entire many-spin wavefunction is used to define the local topological order parameter at the link. We numerically apply this scheme for several spin liquids and show its physical validity.

6 pages. submitted for a proceeding of the conference (HFM2006) as an original paper

References in corpus (2)

• A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet
• Explicit Gauge Fixing for Degenerate Multiplets: A Generic Setup for Topological Orders

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