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/0011388 · Physical review. B, Condensed matter

Collective excitations in ferrimagnetic Heisenberg ladders

Nedko B. Ivanov, Johannes Richter

Published Mar 22, 2001• 15 citations
arXivHTMLPDF

Abstract

We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins ${(S}_{1}>{S}_{2})$ by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase, which is stable for antiferromagnetic interchain couplings ${J}_{\ensuremath{\perp}}>~0$. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground-state parameters (such as the on-site magnetizations and spin-stiffness constant) show a crossover behavior in the weak-coupling region $0<{J}_{\ensuremath{\perp}}<1$. The above peculiarities of the ladder ferrimagnetic state are studied up to second order in the quasiparticle interaction and by a numerical diagonalization of ladders containing up to $N=12$ rungs. The presented results for the ground-state parameters and the excitation spectrum can be used in studies on the low-temperature thermodynamics of ferrimagnetic ladders.

DOI
10.1103/physrevb.63.144429

Related papers

Excitation spectrum of Heisenberg spin ladders

Ted Barnes, Elbio R. Dagotto, José A. Riera +1 more

Heisenberg antiferromagnetic spin ``ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO${)}_{2}$${\mathrm{P}}_{2}$${\mathrm{O}}_{7}$. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-${\mathit{k}}_{0}$${)}^{2}$ (in the strong-coupling limit ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at ${\mathit{k}}_{0}$=\ensuremath{\pi}, and a maximum between ${\mathit{k}}_{1}$=\ensuremath{\pi}/2 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=0) and 0 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=\ensuremath{\infty}). We also give numerical results for the dynamical structure factor S(q,\ensuremath{\omega}), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.

Physical review. B, Condensed matter•Feb 1, 1993•413 citations

Schwinger-boson mean-field method for an alternating-spin (1/2, 1) two-leg ladder

X Y Chen, Qing Jiang, Wen Zhong Shen

We study the low-lying excitations and thermodynamic properties of a ferrimagnetic Heisenberg two-leg ladder, which is composed of alternating-spin (1/2, 1) double chains with antiferromagnetic coupling between the chains. The spin excitation spectra as well as the corresponding energy gaps are calculated by means of the Schwinger-boson mean-field theory. The two interactions between the chains and along the chains play an important role in determining the two branches of the spectrum, not only regarding the size of the low-lying excitation energy gap but also the bandgap between the optical spectrum and the acoustic spectrum. In addition, the two energy gaps and the specific heat have also been calculated at low temperatures.

Journal of Physics Condensed Matter•Feb 3, 2003•2 citations

Low-energy properties of ferrimagnetic two-leg ladders: A Lanczos study

A. Langari, Miguel Angel Martin-Delgado

We apply the Lanczos method to a two-leg ladder with mixed spins of magnitudes ${(S}_{1}{,S}_{2})=(1,1/2)$ located at alternating positions along the ladder. The effect of dimerization $\ensuremath{\gamma}$ is also considered according to two different patterns. A spin-wave theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low-energy excitations of the model. We compute the ground-state energies, ferromagnetic and antiferromagnetic excitation gaps, magnetizations, and correlation functions as a function of ${J}^{\ensuremath{'}}$ and $\ensuremath{\gamma}$ which results into a fine estimate of the phase diagram. The Lanczos results are compared with the SWT analysis and a qualitative agreement is found but with numerical discrepancies. We also study numerically the spin-Peierls instability and find that it is conditional for any value of ${J}^{\ensuremath{'}}\ensuremath{\in}(0,2)$ and both dimerization patterns.

arXiv:cond-mat/0012209•Physical review. B, Condensed matter•Jan 12, 2001•13 citations

Quantum phase transitions in alternating spin-($\frac{1}{2}$, $\frac{5}{2}$) Heisenberg chains

Antônio S F Tenório, R R Montenegro-Filho, M D Coutinho-Filho

The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.

arXiv:1207.5084•Journal of Physics Condensed Matter•Dec 1, 2011•19 citations

Partial Ferrimagnetism in S = 1/2 Heisenberg Ladders with a Ferromagnetic Leg, an Antiferromagnetic Leg, and Antiferromagnetic Rungs

Kazutaka Sekiguchi, Kazuo Hida

Ground-state and finite-temperature properties of $S=1/2$ Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear $σ$ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga--Luttinger liquid with incommensurate magnetic correlation, which is confirmed by a DMRG calculation. The finite-temperature magnetic susceptibility is calculated using the thermal pure quantum state method. It is suggested that the susceptibility diverges as $T^{-2}$ in the ferrimagnetic phases as in the case of ferromagnetic Heisenberg chains.

arXiv:1705.04836•Journal of the Physical Society of Japan•Jul 19, 2017•10 citations

Ground-state phases of a rung-alternated spin−12 Heisenberg ladder

Fatemeh Amiri, Gaoyong Sun, H.-J. Mikeska +1 more

The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.

arXiv:1509.04062•Physical Review B•Nov 20, 2015•16 citations
We study ground-state properties and the low-lying excitations of Heisenberg spin ladders composed of two ferrimagnetic chains with alternating site spins (S1>S2){(S}_{1}>{S}_{2})(S1​>S2​) by using the bosonic Dyson-Maleev formalism and Lanczos numerical techniques. The emphasis is on properties of the ferrimagnetic phase, which is stable for antiferromagnetic interchain couplings J\ensuremath⊥> 0{J}_{\ensuremath{\perp}}>~0J\ensuremath⊥​> 0. There are two basic implications of the underlying lattice structure: (i) the spin-wave excitations form folded acoustic and optical branches in the extended Brillouin zone and (ii) the ground-state parameters (such as the on-site magnetizations and spin-stiffness constant) show a crossover behavior in the weak-coupling region 0<J\ensuremath⊥<10<{J}_{\ensuremath{\perp}}<10<J\ensuremath⊥​<1. The above peculiarities of the ladder ferrimagnetic state are studied up to second order in the quasiparticle interaction and by a numerical diagonalization of ladders containing up to N=12N=12N=12 rungs. The presented results for the ground-state parameters and the excitation spectrum can be used in studies on the low-temperature thermodynamics of ferrimagnetic ladders.
Heisenberg antiferromagnetic spin ``ladders'' (two coupled spin chains) are low-dimensional magnetic systems which for S=1/2 interpolate between half-integer-spin chains, when the chains are decoupled, and effective integer-spin one-dimensional chains in the strong-coupling limit. The spin-1/2 ladder may be realized in nature by vanadyl pyrophosphate, (VO)2{)}_{2})2​P2{\mathrm{P}}_{2}P2​O7{\mathrm{O}}_{7}O7​. In this paper we apply strong-coupling perturbation theory, spin-wave theory, Lanczos techniques, and a Monte Carlo method to determine the ground-state energy and the low-lying excitation spectrum of the ladder. We find evidence of a nonzero spin gap for all interchain couplings ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$>0. A band of spin-triplet excitations above the gap is also analyzed. These excitations are unusual for an antiferromagnet, since their long-wavelength dispersion relation behaves as (k-k0{\mathit{k}}_{0}k0​)2{)}^{2})2 (in the strong-coupling limit ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}J, where J is the in-chain antiferromagnetic coupling). Their band is folded, with a minimum energy at k0{\mathit{k}}_{0}k0​=\ensuremath{\pi}, and a maximum between k1{\mathit{k}}_{1}k1​=\ensuremath{\pi}/2 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=0) and 0 (for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=\ensuremath{\infty}). We also give numerical results for the dynamical structure factor S(q,\ensuremath{\omega}), which can be determined in neutron scattering experiments. Finally, possible experimental techniques for studying the excitation spectrum are discussed.
We study the low-lying excitations and thermodynamic properties of a ferrimagnetic Heisenberg two-leg ladder, which is composed of alternating-spin (1/2, 1) double chains with antiferromagnetic coupling between the chains. The spin excitation spectra as well as the corresponding energy gaps are calculated by means of the Schwinger-boson mean-field theory. The two interactions between the chains and along the chains play an important role in determining the two branches of the spectrum, not only regarding the size of the low-lying excitation energy gap but also the bandgap between the optical spectrum and the acoustic spectrum. In addition, the two energy gaps and the specific heat have also been calculated at low temperatures.
We apply the Lanczos method to a two-leg ladder with mixed spins of magnitudes (S1,S2)=(1,1/2){(S}_{1}{,S}_{2})=(1,1/2)(S1​,S2​)=(1,1/2) located at alternating positions along the ladder. The effect of dimerization $\ensuremath{\gamma}$ is also considered according to two different patterns. A spin-wave theory (SWT) is applied to this model predicting one gapless branch with ferromagnetic properties and another gapful branch with antiferromagnetic nature as low-energy excitations of the model. We compute the ground-state energies, ferromagnetic and antiferromagnetic excitation gaps, magnetizations, and correlation functions as a function of ${J}^{\ensuremath{'}}$ and $\ensuremath{\gamma}$ which results into a fine estimate of the phase diagram. The Lanczos results are compared with the SWT analysis and a qualitative agreement is found but with numerical discrepancies. We also study numerically the spin-Peierls instability and find that it is conditional for any value of ${J}^{\ensuremath{'}}\ensuremath{\in}(0,2)$ and both dimerization patterns.
Quantum phase transitions in alternating spin-(12\frac{1}{2}21​, 52\frac{5}{2}25​) Heisenberg chains
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.
Ground-state and finite-temperature properties of S=1/2S=1/2S=1/2 Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear σσσ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga--Luttinger liquid with incommensurate magnetic correlation, which is confirmed by a DMRG calculation. The finite-temperature magnetic susceptibility is calculated using the thermal pure quantum state method. It is suggested that the susceptibility diverges as T−2T^{-2}T−2 in the ferrimagnetic phases as in the case of ferromagnetic Heisenberg chains.
The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.