Topological Identification of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange

TL;DR

This paper uses quantized Berry phases to identify and distinguish topological phases in a spin-1/2 two-leg ladder with four-spin ring exchange, revealing local objects and topological invariants.

Contribution

It introduces a topological approach using Berry phases to characterize phases in a complex quantum spin ladder model, connecting them to decoupled local objects.

Findings

Berry phase is $ ext{π}$ on a rung in the rung-singlet phase

Berry phase is $ ext{π}$ on a plaquette in the vector-chiral phase

Topologically identical models are connected via adiabatic deformation

Abstract

A spin-1/2 two-leg ladder with four-spin ring exchange is studied by quantized Berry phases, used as local order parameters. Reflecting local objects, non-trivial ($\pi$) Berry phase is founded on a rung for the rung-singlet phase and on a plaquette for the vector-chiral phase. Since the quantized Berry phase is topological invariant for gapped systems with the time reversal symmetry, topologically identical models can be obtained by the adiabatic modification. The rung-singlet phase is adiabatically connected to a decoupled rung-singlet model and the vector-chiral phase is connected to a decoupled vector-chiral model. Decoupled models reveals that the local objects are a local singlet and a plaquette singlet respectively.