Quantized Berry Phases of a Spin-1/2 Frustrated Two-Leg Ladder with Four-Spin Exchange

TL;DR

This paper investigates a frustrated spin-1/2 two-leg ladder with four-spin exchange interactions, demonstrating how quantized Berry phases can identify different quantum phases, including the Haldane phase and vector-chirality phase, revealing their topological nature.

Contribution

The study introduces the use of quantized Berry phases to characterize multiple quantum phases in a frustrated ladder model, highlighting their topological distinctions and novel local objects.

Findings

Berry phase characterizes Haldane, rung-singlet, and vector-chirality phases

Haldane phase is topologically equivalent to S=1 Heisenberg chain

Local objects in vector-chirality phase are products of diagonal singlets

Abstract

A spin-1/2 frustrated two-leg ladder with four-spin exchange interaction is studied by quantized Berry phases. We found that the Berry phase successfully characterizes the Haldane phase in addition to the rung-singlet phase, and the dominant vector-chirality phase. The Hamiltonian of the Haldane phase is topologically identical to the S=1 antiferromagnetic Heisenberg chain. Decoupled models connected to the dominant vector-chirality phase revealed that the local object identified by the non-trivial ($\pi$) Berry phase is the direct product of two diagonal singlets.