Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical mechanical monomer-dimer problem

It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-1/2 Heisenberg diamond and octahedral chains. In addition to monomeric particles assigned within the localized-magnon theory to bound one- and two-magnon eigenstates, the effective monomer-dimer lattice-gas model includes dimeric particles assigned to a singlet-tetramer (singlet-hexamer) state as a cornerstone of dimer-tetramer (tetramer-hexamer) ground state of a spin-1/2 Heisenberg diamond (octahedral) chain. The feasibility of the effective description is confirmed through the exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains display rich ground-state phase diagrams including discontinuous as well as continuous field-driven phase transitions, whereby the specific heat shows in vicinity of the former phase transitions an extraordinary low-temperature peak coming from a highly degenerate manifold of low-lying excitations.

Automated summary

It is demonstrated that effective lattice-gas models can accurately describe the low-temperature features of spin-1/2 Heisenberg diamond and octahedral chains. These models include monomeric and dimeric particles, and their validity is confirmed through exact diagonalization and finite-temperature Lanczos methods. Both quantum spin chains exhibit diverse ground-state phase diagrams, including discontinuous and continuous phase transitions.