Modified strong-coupling treatment of a spin-1/2 Heisenberg trimerized chain developed from the exactly solved Ising-Heisenberg diamond chain

Abstract

Quantum spin-1/2 antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the novel many-body perturbation expansion, which is developed from the exactly solved spin-1/2 Ising-Heisenberg diamond chain preserving correlations between all interacting spins of the trimerized chain unlike the standard perturbation scheme developed on the grounds of noninteracting spin monomers and dimers. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound Cu${}_3$(P${}_2$O${}_6$OH)${}_2$ affording its experimental realization. Within the modified strong-coupling method we have obtained the effective Hamiltonians for the magnetic-field range from zero to one-third plateau, and from one-third plateau to the saturation magnetization. The second-order perturbation theory shows reliable results even for the moderate ratio between weaker dimer-monomer and stronger intradimer coupling constants. We have also examined thermodynamic properties and recovered the low-temperature peak in the specific heat. The accuracy of the developed method is tested through a comparison with numerical density-matrix renormalization group and quantum Monte Carlo simulations. Using the results for the effective Hamiltonian we suggest straightforward procedure for finding the microscopic parameters of one-dimensional trimerized magnetic compounds with strong intradimer and weak monomer-dimer couplings. We found the refined values for the coupling constants of Cu${}_3$(P${}_2$O${}_6$OH)${}_2$ by matching the theoretical results with the available experimental data for the magnetization and magnetic susceptibility in a wide range of temperatures and magnetic fields.

12 pages, 8 figures

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• Ground-state phase diagram and thermodynamics of coupled trimer chains
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• Residual entropy of the dilute Ising chain in a magnetic field
• Trimers in the Extended Hubbard Model