A quantum spin-$\frac{1}{2}$ antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the many-body perturbation expansion, which is developed from the exactly solved spin-$\frac{1}{2}$ Ising-Heisenberg diamond chain preserving correlations between all interacting spins of the trimerized chain. It is evidenced that this perturbation approach is superior with respect to the standard perturbation scheme developed from a set of noninteracting spin monomers and dimers, and its accuracy even coincides, up to a moderate ratio of the coupling constants, with state-of-the-art numerical techniques. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound ${\mathrm{Cu}}_3{\left({\mathrm{P}}_2{\mathrm{O}}_6\mathrm{OH}\right)}_2$ affording its experimental realization. Within the modified strong-coupling method we have obtained the effective Hamiltonians for the magnetic field range from zero to the one-third plateau, and from the one-third plateau to the saturation magnetization. The unconventional second-order perturbation theory provides extremely accurate results for both critical fields of the intermediate one-third plateau up to a moderate ratio of the coupling constants as convincingly evidenced through a comparison with numerical density-matrix renormalization group data. It is shown that the derived effective Hamiltonian also provides at low enough temperatures sufficiently accurate results for magnetization curves and thermodynamic properties as corroborated through a comparison with quantum Monte Carlo simulations. Using the results for the effective Hamiltonian, we additionally suggest a 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 ${\mathrm{Cu}}_3{\left({\mathrm{P}}_2{\mathrm{O}}_6\mathrm{OH}\right)}_2$ 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.

• Received 25 January 2021
• Revised 15 April 2021
• Accepted 3 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.184415