We present a condition in which the dimer-monomer state is exactly the ground state of an extended diamond chain with spin magnitude 1/2. The Hamiltonian of the extended diamond chain includes next-nearest-neighbor exchange interactions and distortions, where the spin magnitude of the spin pair on a singlet dimer is not generally conserved. The method of deriving the condition is based on representing the Hamiltonian in a complete square form. The dimer-monomer ground state is found even if the Hamiltonian has no space-reflection symmetries.We present a condition in which the dimer-monomer state is exactly the ground state of an extended diamond chain with spin magnitude 1/2. The Hamiltonian of the extended diamond chain includes next-nearest-neighbor exchange interactions and distortions, where the spin magnitude of the spin pair on a singlet dimer is not generally conserved. The method of deriving the condition is based on representing the Hamiltonian in a complete square form. The dimer-monomer ground state is found even if the Hamiltonian has no space-reflection symmetries.

arXiv:1706.06350Journal of the Physical Society of JapanAug 22, 20172 citations

A Monte Carlo study of coupled Ising chains

D. P. Landau, Tom Graim

Annals of the Israel Physical SocietyJan 1, 19780 citations

Tensor network investigation of the monomer-dimer model on the honeycomb lattice

De-Zhang Li, Jie Liu, Xin Wang

The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field $H_{\rm{ex}}=4J$ , and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field $H_{\rm{ex}}=4J$, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.

arXiv:2609.07899Sep 7, 20260 citations

Modified strong-coupling treatment of a spin- 12 Heisenberg trimerized chain developed from the exactly solved Ising-Heisenberg diamond chain

Taras Verkholyak, Jozef Strečka

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 ${\mathrm{Cu}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{6}\mathrm{OH})}_{2}$ affording its experimental realization. Within the modified strong-coupling method we have obtained the effective Hamiltonians for the magnetic field range from zero to 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 ${\mathrm{Cu}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{6}\mathrm{OH})}_{2}$ 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.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 ${\mathrm{Cu}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{6}\mathrm{OH})}_{2}$ affording its experimental realization. Within the modified strong-coupling method we have obtained the effective Hamiltonians for the magnetic field range from zero to 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 ${\mathrm{Cu}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{6}\mathrm{OH})}_{2}$ 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:2101.11926Physical review. B./Physical review. BMay 14, 202115 citations

H_{\rm{ex}}=4J

, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.

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}{({\mathrm{P}}_{2}{\mathrm{O}}_{6}\mathrm{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 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}{({\mathrm{P}}_{2}{\mathrm{O}}_{6}\mathrm{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.