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.

arXiv comment12 pages, 8 figures

References in corpus (23)

• Stochastic series expansion method with operator-loop update
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Spin-lattice coupling in frustrated antiferromagnets
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
• Magnetic Properties of the Spin-1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Trimerized Heisenberg Chain:
• Multi-step approach to microscopic models for frustrated quantum magnets - the case of the natural mineral azurite
• Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains
• Generalized algebraic transformations and exactly solvable classical-quantum models
• Plateau of the Magnetization Curve of the S=1/2 Ferromagnetic-Ferromagnetic-Antiferromagnetic Spin Chain
• Frustrated trimer chain model and Cu3Cl6(H2O)2 2H8C4SO2 in a magnetic field
• Neutron Scattering and Magnetic Observables for S = 1/2 Molecular Magnets
• Dynamic and thermodynamic properties of the generalised diamond chain model for azurite
• Thermodynamic properties of a tetramer ferro-ferro-antiferro-antiferromagnetic Ising-Heisenberg bond alternating chain as a model system for Cu(3-Clpy)${}_2$(N${}_3$)${}_2$
• Quantum vs. Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains
• Thermodynamics of Spin-1/2 AF-AF-F and F-F-AF Trimerized Quantum Heisenberg Chains
• Existence of the magnetization plateau in a class of exactly solvable Ising-Heisenberg chains
• Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario
• A Strong-Coupling Approach to the Magnetization Process of Polymerized Quantum Spin Chains
• Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field
• Fractional magnetization plateaux of the spin-1/2 Heisenberg orthogonal-dimer chain revisited: strong-coupling approach developed from the exactly solved Ising-Heisenberg model
• Spin structure factors and valence-bond-solid states of the trimerized Heisenberg chains in a magnetic field
• Effective low-energy description of almost Ising-Heisenberg diamond chain

Cited by in corpus (6)

• Fractional and composite excitations of antiferromagnetic quantum spin trimer chains
• Bulk and edge dynamics of a 2D Affleck-Kennedy-Lieb-Tasaki model
• Ground-state phase diagram and thermodynamics of coupled trimer chains
• Quantum Information Resources in Spin-1 Heisenberg Dimer Systems
• Residual entropy of the dilute Ising chain in a magnetic field
• Trimers in the Extended Hubbard Model