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/0605370

Crossover of spectral features from Dimerized to Haldane behavior in alternating antiferromagnetic-ferromagnetic spin-half chains

Weihong Zheng, Chris J. Hamer, Rajiv R. P. Singh

Published May 15, 2006• 0 citations
arXivHTMLPDF

Abstract

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$. For small $|λ|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|λ|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

DOI
10.48550/arxiv.cond-mat/0605370

Related papers

Spectral properties of alternating antiferromagnetic-ferromagnetic spin-half chains and the emergence of composite spin-one behavior

Weihong Zheng, Chris J. Hamer, Rajiv R. P. Singh

We study the spectral properties of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $\ensuremath{-}\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}J$. The crossover from the gapped dimerized spectra at small $\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}$ to the spin-one chain behavior at large $\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}$ is signaled by the merging of the one-particle state with the bottom of the continuum, and its vanishing spectral weight, near $k=0$. At large $\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}$, the model represents a class of spin-one chains with varying degrees of spatial and temporal compositeness and provides an excellent quantitative description of the neutron scattering spectra for such materials as ${(\mathrm{C}{\mathrm{D}}_{3})}_{2}\mathrm{N}{\mathrm{D}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{3}$ and $\mathrm{IPA}\text{\ensuremath{-}}\mathrm{Cu}{\mathrm{Cl}}_{3}$.

Physical Review B•Nov 13, 2006•8 citations

Redistribution of spectral weight in Haldane chains doped with spin- 12 moments

Stefan Weßel, Stephan Haas

We study the evolution of the dynamical spin structure factor in a spin-1 antiferromagnetic Heisenberg chain which is randomly doped with spin-1/2 moments. Using stochastic series expansion quantum Monte Carlo simulations combined with the maximum entropy method, we monitor the crossover from the spin-1 chain, dominated by a single resonance at the Haldane energy, to the spin-1/2 chain with a continuum of spinon states which diverges at zero frequency. Upon increasing the doping level, spectral weight is rapidly transferred from the Haldane peak to lower energies. If the exchange couplings between the spin-1/2 substituents and the spin-1 sites of the host are sufficiently small, finite-frequency bound states are observed below the spin gap for small doping concentrations.

arXiv:cond-mat/0106385•Physical review. B, Condensed matter•Mar 8, 2002•3 citations

Finite temperature properties of alternating ferro-antiferromagnetic Heisenberg chains

Niklas Casper, Wolfram Brenig

We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitrary exchange couplings we show that the dynamic structure factor, obtained from quantum Monte Carlo, scales between triplons and a Haldane chain spectrum. Finally, we contrast our findings for the spin gap versus the exchange couplings against existing literature.

arXiv:2001.04696•Jan 14, 2020•0 citations

A note on Haldane’s conjecture

Li-Hua Pan, Chang-De Gong

According to Haldane’s conjecture, there is a spin gap of the excitation spectrum in integer Heisenberg spin chains whereas half-integer spin chains have a gapless excitation spectrum. In an earlier publication (Hung and Gong 2005 Phys. Rev. B 71 054413), the Haldane gap and other properties of the spin-1 system are explained using a spin-1/2 alternating bond chain model. The ferromagnetic–ferromagnetic–antiferromagnetic Heisenberg spin-1/2 chain is expected to behave similarly to the uniform spin-3/2 Heisenberg chain for strong ferromagnetic coupling. And the general nonuniform spin-1/2 chain may be used to explain the properties of the integer and half-integer high spin- S chains, consistently. In this paper, we provide a detailed numerical verification for the above problems.

Journal of Physics Condensed Matter•Apr 25, 2008•3 citations

Dynamical structure factors of S=1 bond-alternating Heisenberg chains

Takahumi Suzuki, Sei-ichiro Suga

We calculate the dynamical structural factor of the $S=1$ bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~{q}_{c}$ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in $0<~q<~{q}_{c}.$ As the bond-alternation becomes strong, ${q}_{c}$ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is $93%,$ which is slightly smaller than that in the $S=1$ Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.

arXiv:cond-mat/0309178•Physical review. B, Condensed matter•Oct 17, 2003•5 citations

Magnetic excitation spectrum of dimerized antiferromagnetic chains

Götz Silvester Uhrig, Heinz J. Schulz

Motivated by recent measurements on CuGe${\mathrm{O}}_{3}$, the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.

arXiv:cond-mat/9606001•Physical review. B, Condensed matter•Oct 1, 1996•170 citations
We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings JJJ and −∣λ∣J-|λ|J−∣λ∣J as a power series in λλλ. For small ∣λ∣|λ|∣λ∣, the gapped one-particle spectrum has a maximum at k=0k=0k=0 and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As ∣λ∣|λ|∣λ∣ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from k=0k=0k=0, the one particle states merge with the bottom of the continuum near k=0k=0k=0, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large ∣λ∣|λ|∣λ∣ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.
We study the spectral properties of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings JJJ and $\ensuremath{-}\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}J$. The crossover from the gapped dimerized spectra at small $\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}$ to the spin-one chain behavior at large $\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}$ is signaled by the merging of the one-particle state with the bottom of the continuum, and its vanishing spectral weight, near k=0k=0k=0. At large $\ensuremath{\mid}\ensuremath{\lambda}\ensuremath{\mid}$, the model represents a class of spin-one chains with varying degrees of spatial and temporal compositeness and provides an excellent quantitative description of the neutron scattering spectra for such materials as (CD3)2ND2CuCl3{(\mathrm{C}{\mathrm{D}}_{3})}_{2}\mathrm{N}{\mathrm{D}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{3}(CD3​)2​ND2​CuCl3​ and $\mathrm{IPA}\text{\ensuremath{-}}\mathrm{Cu}{\mathrm{Cl}}_{3}$.
We study the evolution of the dynamical spin structure factor in a spin-1 antiferromagnetic Heisenberg chain which is randomly doped with spin-1/2 moments. Using stochastic series expansion quantum Monte Carlo simulations combined with the maximum entropy method, we monitor the crossover from the spin-1 chain, dominated by a single resonance at the Haldane energy, to the spin-1/2 chain with a continuum of spinon states which diverges at zero frequency. Upon increasing the doping level, spectral weight is rapidly transferred from the Haldane peak to lower energies. If the exchange couplings between the spin-1/2 substituents and the spin-1 sites of the host are sufficiently small, finite-frequency bound states are observed below the spin gap for small doping concentrations.
We present a study of the spin-1/2 Heisenberg chain with alternating ferro- and antiferromagnetic exchange, focusing on the role of the exchange couplings to cover both, dimer and Haldane limit. Employing a complementary combination of perturbation theory and quantum Monte Carlo simulation, we report results for the magnetic susceptibility as well as the dynamic structure factor over a wide range of coupling constants and for different temperatures to extract the spin gap. For a small ferromagnetic coupling, we find good agreement between perturbation theory and quantum Monte Carlo. For arbitrary exchange couplings we show that the dynamic structure factor, obtained from quantum Monte Carlo, scales between triplons and a Haldane chain spectrum. Finally, we contrast our findings for the spin gap versus the exchange couplings against existing literature.
According to Haldane’s conjecture, there is a spin gap of the excitation spectrum in integer Heisenberg spin chains whereas half-integer spin chains have a gapless excitation spectrum. In an earlier publication (Hung and Gong 2005 Phys. Rev. B 71 054413), the Haldane gap and other properties of the spin-1 system are explained using a spin-1/2 alternating bond chain model. The ferromagnetic–ferromagnetic–antiferromagnetic Heisenberg spin-1/2 chain is expected to behave similarly to the uniform spin-3/2 Heisenberg chain for strong ferromagnetic coupling. And the general nonuniform spin-1/2 chain may be used to explain the properties of the integer and half-integer high spin- S chains, consistently. In this paper, we provide a detailed numerical verification for the above problems.
We calculate the dynamical structural factor of the S=1S=1S=1 bond-alternating Heisenberg chain. In the Haldane phase, the lowest excited states form the lower edge of the multimagnon continuum in 0< q< qc0<~q<~{q}_{c}0< q< qc​ and the one-magnon mode in ${q}_{c}<~q<~\ensuremath{\pi}.$ As the system approaches the gapless point, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}$ and the largest integrated intensity of the one-magnon mode is decreased. In the singlet-dimer phase, the one-magnon mode appears in 0< q< qc.0<~q<~{q}_{c}.0< q< qc​. As the bond-alternation becomes strong, qc{q}_{c}qc​ shifts towards $q=\ensuremath{\pi}.$ In the antiferromagnetic-ferromagnetic bond-alternation region with a strong ferromagnetic coupling, the lowest excited states form the lower edge of the multimagnon continuum in $0<~q<~0.2\ensuremath{\pi}$ and $0.8\ensuremath{\pi}<~q<~\ensuremath{\pi},$ and the one-magnon mode appears in $0.2\ensuremath{\pi}<q<0.8\ensuremath{\pi}.$ The largest integrated intensity of the one-magnon mode is 9393%,93 which is slightly smaller than that in the S=1S=1S=1 Haldane-gap system. We further discuss the dynamical structural factor in connection with the inelastic neutron-scattering experiments.
Motivated by recent measurements on CuGeO3{\mathrm{O}}_{3}O3​, the spectrum of magnetic excitations of an antiferromagnetic S=12S=\frac{1}{2}S=21​ chain with alternating coupling strength is investigated. Wave-vector-dependent magnons and a continuum with square-root behavior at the band edges are found. The spectral density of the continua is calculated. Spin-rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. The existence of (anti)bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum a quintuplet.