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

AIP conference proceedings

Spin Dynamics of a Dimerized Heisenberg Chain

M. Drawid, J. W. Halleý

Published Jan 1, 1976• 5 citations
Publisher

Abstract

We describe an approximate Green function decoupling theory for the dynamics of a dimerized Heisenberg chain. The theory retains the rotational invariance of the spin system in the approximations as Bulaevskii's approximate theory does not. We find that, within the approximations used, the excitation spectrum of the chain can be described as consisting of two branches: A band with a gap of k = 0 and a second, acoustic, band with no gap. The acoustic band does not appear in the Bulaevskii theory. We discuss the possible relevance of this result to experiments.

DOI
10.1063/1.2946072

Related papers

Renormalization group and other calculations for the one-dimensional spin-1/2 dimerized Heisenberg antiferromagnet

J. N. Fields, Henk W. J. Blöte, J. C. Bonner

A zero-temperature renormalization group (RG) approach is applied to the one-dimensional, spin-1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest-lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin-1/2 XY dimerized chain.

Journal of Applied Physics•Mar 1, 1979•50 citations

Spectral excitations in the one-dimensional spin-½ dimerized Heisenberg chain: A renormalization-group approach

J. N. Fields

A zero-temperature lattice renormalization-group calculation is presented and applied to the antiferromagnetic one-dimensional dimerized spin-\textonehalf{} Heisenberg chain. The calculation indicates the existence of a gap in the spectrum of the dimer system, which vanishes only in the limit of a uniform spin chain. To improve the accuracy of the numerical estimates of the ground-state energy and gap, an iterative extension of finite-chain techniques is also applied. These approximate techniques are checked against the dimerized $\mathrm{XY}$ chain, for which an exact solution is found.

Physical review. B, Condensed matter•Mar 1, 1979•35 citations

Approximate calculation of the excitation spectrum of the Heisenberg linear chain

B. Sriram Shastry, Chanchal K. Majumdar

An approximate calculation of the excitation spectrum of the Heisenberg linear chain is performed by the Green's-function technique. Apart from the usual transverse Green's function, a longitudinal Green's function is also found useful. The decoupling procedure is not based on the two-sublattice picture, but utilizes the knowledge of known exact results about the ground state of the linear chain and the insight obtained from a model with explicitly known ground state. The equations are solved in a self-consistent manner, and the spectrum, except near the edge of the Brillouin zone, compares well the exact des Cloizeaux-Pearson result. We also provide an expression for the intensity for neutron-scattering studies; this can be checked against measurements on Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2N(${\mathrm{C}}_{5}$${\mathrm{D}}_{5}$) (CPC).

Physical review. B, Solid state•Oct 1, 1975•2 citations

Temperature Dependence of Energy Gaps in Spin—1／2 Dimerized Heisenberg Chain

江学范, 陈鸿

We present a method which combines a thermal coherent state approach with a self-consistent quantum theory to investigate the spin-1/2 dimerized antiferromagnetic Heisenberg chain.It is found that both excitation gaps between the ground state and two lowest excited modes,the triplet one-magnon excitation and the singlet two-magnon bound state decrease monotonically with increasing temperature.Our results are consitent with those obtained from the other approximations.

Chinese Physics Letters•Jan 1, 2002•0 citations

Temperature Dependence of Energy Gaps in Spin-1/2 Dimerized Heisenberg Chain

Jiang Xue-Fan, Xing Ding-Yu, Chen Hong

We present a method which combines a thermal coherent state approach with a self-consistent quantum theory to investigate the spin-1/2 dimerized antiferromagnetic Heisenberg chain. It is found that both excitation gaps between the ground state and two lowest excited modes, the triplet one-magnon excitation and the singlet two-magnon bound state decrease monotonically with increasing temperature. Our results are consistent with those obtained from the other approximations.

Chinese Physics Letters•Mar 26, 2002•2 citations

Elementary excitations in dimerized and frustrated Heisenberg chains

G. Bouzerar, A. P. Kampf, G. I. Japaridze

We present a detailed numerical analysis of the low-energy excitation spectrum of a frustrated and dimerized spin $S=1/2$ Heisenberg chain. In particular, we show that in the commensurate spin-Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory. We discuss the relevance of our data in connection with recent experiments on ${\mathrm{CuGeO}}_{3},$ ${\mathrm{NaV}}_{2}{\mathrm{O}}_{5},$ and $(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}$.

arXiv:cond-mat/9801046•Physical review. B, Condensed matter•Aug 1, 1998•81 citations
We describe an approximate Green function decoupling theory for the dynamics of a dimerized Heisenberg chain. The theory retains the rotational invariance of the spin system in the approximations as Bulaevskii's approximate theory does not. We find that, within the approximations used, the excitation spectrum of the chain can be described as consisting of two branches: A band with a gap of k = 0 and a second, acoustic, band with no gap. The acoustic band does not appear in the Bulaevskii theory. We discuss the possible relevance of this result to experiments.
A zero-temperature renormalization group (RG) approach is applied to the one-dimensional, spin-1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest-lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin-1/2 XY dimerized chain.
A zero-temperature lattice renormalization-group calculation is presented and applied to the antiferromagnetic one-dimensional dimerized spin-\textonehalf{} Heisenberg chain. The calculation indicates the existence of a gap in the spectrum of the dimer system, which vanishes only in the limit of a uniform spin chain. To improve the accuracy of the numerical estimates of the ground-state energy and gap, an iterative extension of finite-chain techniques is also applied. These approximate techniques are checked against the dimerized XY\mathrm{XY}XY chain, for which an exact solution is found.
An approximate calculation of the excitation spectrum of the Heisenberg linear chain is performed by the Green's-function technique. Apart from the usual transverse Green's function, a longitudinal Green's function is also found useful. The decoupling procedure is not based on the two-sublattice picture, but utilizes the knowledge of known exact results about the ground state of the linear chain and the insight obtained from a model with explicitly known ground state. The equations are solved in a self-consistent manner, and the spectrum, except near the edge of the Brillouin zone, compares well the exact des Cloizeaux-Pearson result. We also provide an expression for the intensity for neutron-scattering studies; this can be checked against measurements on CuCl2{\mathrm{Cl}}_{2}Cl2​\ifmmode\cdot\else\textperiodcentered\fi{}2N(C5{\mathrm{C}}_{5}C5​D5{\mathrm{D}}_{5}D5​) (CPC).
We present a detailed numerical analysis of the low-energy excitation spectrum of a frustrated and dimerized spin S=1/2S=1/2S=1/2 Heisenberg chain. In particular, we show that in the commensurate spin-Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory. We discuss the relevance of our data in connection with recent experiments on CuGeO3,{\mathrm{CuGeO}}_{3},CuGeO3​, NaV2O5,{\mathrm{NaV}}_{2}{\mathrm{O}}_{5},NaV2​O5​, and (VO)2P2O7(\mathrm{VO}{)}_{2}{\mathrm{P}}_{2}{\mathrm{O}}_{7}(VO)2​P2​O7​.