Quantized Berry Phases as Local Order Parameters of Quantum Liquids

TL;DR

This paper introduces a method using quantized Berry phases as local order parameters to characterize gapped quantum liquids, providing a new way to identify ground state patterns in complex quantum systems.

Contribution

The paper presents a general scheme for using quantized Berry phases as local order parameters, applied to frustrated Heisenberg models and extended SSH models.

Findings

Quantized Berry phases are 0 or π, indicating local singlet and dimer bond patterns.

The scheme successfully characterizes different phases in complex quantum models.

Potential applications extend to various correlated electron systems.

Abstract

We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with frustrations and two dimensional extended Su-Schrieffer-Heeger models associated with a random dimer covering. In each phases, the quantized Berry phases, as 0 or $\pi$, describe the ground state texture pattern of local singlet bonds and dimer bonds. Also possible applications to large classes of correlated electron systems are discussed.