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:cond-mat/0105096 · Physical review. B, Condensed matter

Magnetism of a tetrahedral cluster spin chain

Wolfram Brenig, K. W. Becker

Published Nov 12, 2001• 57 citations
arXivHTMLPDF

Abstract

We discuss the magnetic properties of a dimerized and completely frustrated tetrahedral spin-1/2 chain. Using a combination of exact diagonalization and bond-operator theory the quantum phase diagram is shown to incorporate a singlet product, a dimer, and a Haldane phase. In addition we consider one- and two-triplet excitations in the dimer phase and evaluate the magnetic Raman cross section which is found to be strongly renormalized by the presence of a two-triplet bound state. The link to a novel tellurate materials is clarified.

DOI
10.1103/physrevb.64.214413

Related papers

Quantum dimer phases in a frustrated spin ladder

T. Vekua, A. Honecker

The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.

•Jan 24, 2006•0 citations

Quantum dimer phases in a frustrated spin ladder: Effective field theory approach and exact diagonalization

T. Vekua, A. Honecker

The phase diagram of a frustrated $S=1∕2$ antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and in-chain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.

arXiv:cond-mat/0601545•Physical Review B•Jun 14, 2006•58 citations

Behavior of a frustrated quantum spin chain with bond dimerization

Tota Nakamura, Satoshi Takada

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully frustrated point, where a localized kink and a freely mobile antikink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. They finally collapse to a local triplet at a sufficient value of the dimerization. The wave function of the bound state, the consequential gap enhancement, and the localization length of the bound state were obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. We also obtained the dispersion relation of the local triplet excitation for the entire phase space. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional ${\mathrm{J}}_{1}$-${\mathrm{J}}_{2}$ model, or the frustrated ladder model.

arXiv:cond-mat/9612066•Physical review. B, Condensed matter•Jun 1, 1997•5 citations

Spectrum of elementary and collective excitations in the dimerized S=1/2 Heisenberg chain with frustration

Pavel V. Shevchenko, Valeri N. Kotov, Oleg P. Sushkov

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet $(S=0)$ and triplet $(S=1)$ modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.

arXiv:cond-mat/9901302•Physical review. B, Condensed matter•Aug 1, 1999•23 citations

BOUND STATES IN DIMERIZED AND FRUSTRATED HEISENBERG CHAINS

G. Bouzerar, S. SIL

Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.

arXiv:cond-mat/9805042•International Journal of Modern Physics B•Aug 10, 2001•3 citations

Ground-state phase diagram of a spin- 12 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases

Shunsuke Furukawa, Masahiro Sato, Shigeki Onoda +1 more

The ground-state phase diagram of a spin-$\frac{1}{2}$ XXZ chain with competing ferromagnetic nearest-neighbor (${J}_{1}<0$) and antiferromagnetic second-neighbor (${J}_{2}>0$) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.

arXiv:1207.1059•Physical Review B•Sep 12, 2012•120 citations
We discuss the magnetic properties of a dimerized and completely frustrated tetrahedral spin-1/2 chain. Using a combination of exact diagonalization and bond-operator theory the quantum phase diagram is shown to incorporate a singlet product, a dimer, and a Haldane phase. In addition we consider one- and two-triplet excitations in the dimer phase and evaluate the magnetic Raman cross section which is found to be strongly renormalized by the presence of a two-triplet bound state. The link to a novel tellurate materials is clarified.
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
The phase diagram of a frustrated S=1∕2S=1∕2S=1∕2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and in-chain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully frustrated point, where a localized kink and a freely mobile antikink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. They finally collapse to a local triplet at a sufficient value of the dimerization. The wave function of the bound state, the consequential gap enhancement, and the localization length of the bound state were obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. We also obtained the dispersion relation of the local triplet excitation for the entire phase space. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J1{\mathrm{J}}_{1}J1​-J2{\mathrm{J}}_{2}J2​ model, or the frustrated ladder model.
We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet (S=0)(S=0)(S=0) and triplet (S=1)(S=1)(S=1) modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.
Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.
The ground-state phase diagram of a spin-12\frac{1}{2}21​ XXZ chain with competing ferromagnetic nearest-neighbor (J1<0{J}_{1}<0J1​<0) and antiferromagnetic second-neighbor (J2>0{J}_{2}>0J2​>0) exchange couplings is studied by means of the infinite time evolving block decimation algorithm and effective field theories. For the SU(2)-symmetric (Heisenberg) case, we show that the nonmagnetic phase in the range $\ensuremath{-}4<{J}_{1}/{J}_{2}<0$ has a small but finite ferromagnetic dimer order. We argue that this spontaneous dimer order is associated with effective spin-1 degrees of freedom on dimerized bonds, which collectively form a valence bond solid state as in the spin-1 antiferromagnetic Heisenberg chain (the Haldane spin chain). We thus call this phase the Haldane dimer phase. With easy-plane anisotropy, the model exhibits a variety of phases including the vector chiral phase with gapless excitations and the even-parity dimer and N\'eel phases with gapped excitations, in addition to the Haldane dimer phase. Furthermore, we show the existence of gapped phases with coexisting orders in narrow regions that intervene between the gapless chiral phase and any one of Haldane dimer, even-parity dimer, and N\'eel phases. Possible implications for quasi-one-dimensional edge-sharing cuprates are discussed.