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

TL;DR

This paper introduces a method using quantized Berry phases to locally characterize gapped spin liquids in frustrated spin systems, providing a new topological order parameter applicable to these complex quantum states.

Contribution

It proposes a novel local topological characterization scheme for spin liquids using Berry phases, applicable to frustrated Heisenberg models with a finite gap.

Findings

Successfully applied the scheme to various spin liquids

Demonstrated the physical validity of the local topological order parameter

Provided a new tool for analyzing topological properties in frustrated 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.