Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1706.06350 · Journal of the Physical Society of Japan

Dimer-Monomer Ground State for Extended Spin-1/2 Diamond Chain

Ken'ichi Takano

Published Aug 22, 2017• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.7566/jpsj.86.093705

Related papers

Exact Dimer State of Quantum Spin Chain with Long-Range Interactions

Hiroki Nakano, Minoru Takahashi

Quantum Heisenberg antiferromagnets in one dimension with long-range interactions are studied; a Hamiltonian which has dimer states composed of nearest-neighbor singlet pairs as eigenstates of the system is obtained. We also obtain sufficient conditions under which the eigenstates are the ground states. We propose a model which is very similar to the Haldane-Shastry model but has the dimer ground states.

Journal of the Physical Society of Japan•Aug 15, 1995•6 citations

Quantum phase with spontaneous translational symmetry breaking in an extended diamond chain

Hironori Yamaguchi, Shunsuke C. Furuya, Y. Tominaga +2 more

We report the experimental realization of a spin-1/2 extended diamond chain in a verdazyl-Cu complex, where competing interactions and lattice distortions give rise to exotic quantum phases. The magnetic properties exhibit a zero-field energy gap and 1/2 magnetization plateau, which is explained by a dimer-monomer model. Considering the effective interactions between the monomers, three types of dimer-dimer phases are expected to appear as the ground state, depending on the magnitude of the lattice distortions. By mapping to the nonlinear sigma model, three phases are distinguished topologically, and a symmetry-protected topological phase equivalent to the Haldane phase is identified. Furthermore, a nontrivial magnetization is observed above the 1/2 plateau region, suggesting a gapped dimer phase accompanied by a spontaneous breaking of translational symmetry. The discovery of this rare quantum state has broad implications for strongly correlated systems, topological matter, and quantum information science, where symmetry and topology play crucial roles.

arXiv:2509.08202•Physical review. B./Physical review. B•Aug 21, 2025•1 citation

Effect of monomer-monomer interactions on the phase diagrams of the S = 1/2 distorted diamond type quantum spin chain

Kiyomi Okamoto, Takashi Tonegawa, Tôru Sakai

By use of mainly the exact diagonalization and the level spectroscopy method, we investigate the ground-state phase diagrams of the S = 1/2 distorted diamond type quantum spin chain with the monomer-monomer interactions and/or ferromagnetic interactions for the zero magnetic field case, as well as the M = M s /3 case and the M = (2/3) M s case, where M is the total magnetization and M s is the saturation magnetization. The magnetization plateau at M = M s /3 vanishes in the region where the ferromagnetic interaction is rather strong. The monomer-monomer interaction remarkably stabilizes the magnetization plateau at M = (2/3) M s .

arXiv:1510.04913•Journal of Physics Conference Series•Feb 5, 2016•2 citations

Long-Ranged Interacting Quantum Spin Chain with Exact Dimer State

Hiroki Nakano, Minoru Takahashi

One-dimensional S =1/2 and S =1 spin systems with interactions between not only nearest-neighbor pairs of spins but also longer-range pairs are studied. We find the necessary and sufficient conditions between the coupling constants of the interactions under which the dimer state is an eigenstate of the system. We present a sufficient condition of the dimer ground state for extracted Hamiltonians. Properties of the ground state outside the dimer phase are also discussed by means of an analytical way and numerical diagonalizations.

Journal of the Physical Society of Japan•Jan 15, 1997•8 citations

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

Jozef Strečka, Taras Verkholyak, Johannes Richter +3 more

It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-$\frac{1}{2}$ 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-$\frac{1}{2}$ 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.

arXiv:2110.07958•Physical review. B./Physical review. B•Feb 15, 2022•19 citations

Quantum Phase Transitions in Alternating-Bond Mixed Diamond Chains with Spins 1 and 1/2

Kazuo Hida, Ken'ichi Takano, Hidenori Suzuki

We investigate the mixed diamond chain composed of spins 1 and 1/2 when the exchange interaction is alternatingly distorted. Depending on the strengths of frustration and distortion, this system has various ground states. Each ground state consists of an array of spin clusters separated by singlet dimers by virtue of an infinite number of local conservation laws. We determine the ground state phase diagram by numerically analyzing each spin cluster. In particular for strong distortion, we find an infinite series of quantum phase transitions by the cluster expansion method and conformal field theory. This leads to the infinite series of steps in the behavior of the Curie constant and residual entropy.

arXiv:0911.3838•Journal of the Physical Society of Japan•Mar 25, 2010•14 citations
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 report the experimental realization of a spin-1/2 extended diamond chain in a verdazyl-Cu complex, where competing interactions and lattice distortions give rise to exotic quantum phases. The magnetic properties exhibit a zero-field energy gap and 1/2 magnetization plateau, which is explained by a dimer-monomer model. Considering the effective interactions between the monomers, three types of dimer-dimer phases are expected to appear as the ground state, depending on the magnitude of the lattice distortions. By mapping to the nonlinear sigma model, three phases are distinguished topologically, and a symmetry-protected topological phase equivalent to the Haldane phase is identified. Furthermore, a nontrivial magnetization is observed above the 1/2 plateau region, suggesting a gapped dimer phase accompanied by a spontaneous breaking of translational symmetry. The discovery of this rare quantum state has broad implications for strongly correlated systems, topological matter, and quantum information science, where symmetry and topology play crucial roles.
By use of mainly the exact diagonalization and the level spectroscopy method, we investigate the ground-state phase diagrams of the S = 1/2 distorted diamond type quantum spin chain with the monomer-monomer interactions and/or ferromagnetic interactions for the zero magnetic field case, as well as the M = M s /3 case and the M = (2/3) M s case, where M is the total magnetization and M s is the saturation magnetization. The magnetization plateau at M = M s /3 vanishes in the region where the ferromagnetic interaction is rather strong. The monomer-monomer interaction remarkably stabilizes the magnetization plateau at M = (2/3) M s .
One-dimensional S =1/2 and S =1 spin systems with interactions between not only nearest-neighbor pairs of spins but also longer-range pairs are studied. We find the necessary and sufficient conditions between the coupling constants of the interactions under which the dimer state is an eigenstate of the system. We present a sufficient condition of the dimer ground state for extracted Hamiltonians. Properties of the ground state outside the dimer phase are also discussed by means of an analytical way and numerical diagonalizations.
It is evidenced that effective lattice-gas models of hard-core monomers and dimers afford a proper description of low-temperature features of spin-12\frac{1}{2}21​ 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-12\frac{1}{2}21​ 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.
We investigate the mixed diamond chain composed of spins 1 and 1/2 when the exchange interaction is alternatingly distorted. Depending on the strengths of frustration and distortion, this system has various ground states. Each ground state consists of an array of spin clusters separated by singlet dimers by virtue of an infinite number of local conservation laws. We determine the ground state phase diagram by numerically analyzing each spin cluster. In particular for strong distortion, we find an infinite series of quantum phase transitions by the cluster expansion method and conformal field theory. This leads to the infinite series of steps in the behavior of the Curie constant and residual entropy.