Z$_2$ topological number of local quantum clusters in the orthogonal dimer model

TL;DR

This paper investigates the Z₂ topological number via Berry phase to identify local quantum clusters in frustrated systems, exemplified by the orthogonal dimer model and related materials, revealing phases like dimer- and plaquette-singlet states.

Contribution

It introduces a method using Z₂ topological numbers to characterize local quantum clusters in frustrated systems, applicable even when the ground state is unknown.

Findings

Z₂ topological number distinguishes different quantum cluster phases

Identification of dimer- and plaquette-singlet phases in specific models

Application to experimentally realized materials like SrCu₂(BO₃)₂

Abstract

We have studied the $Z_2$ topological number defined by the Berry phase for the gapped frustrated systems including the orthogonal dimer model which has a direct product state of local quantum clusters as the exact ground state. The $Z_2$ topological number can clarify what kind of the local quantum clusters is formed to lift the macroscopic degeneracy due to frustration, even when the exact ground state is unknown. As a demonstration, the dimer-singlet and plaquette-singlet phase are identified by two kinds of Z$_2$ topological numbers in the Shastry-Sutherland model and its generalization realized experimentally as SrCu$_2$(BO$_3$)$_2$ and CaV$_4$O$_9$.