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

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${}_9$.

6 pages, 4 figures, Proceedings of the International Conference on Frustration in Condensed Matter (ICFCM) 2011

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Cited by in corpus (2)

• Symmetry Protected Quantization and Bulk-Edge Correspondence of Massless Dirac Fermions: Application to Fermionic Shastry-Sutherland Model
• Fractionally quantized Berry phases of magnetization plateaux in spin-$1/2$ Heisenberg multimer chains