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

Journal of Physics A Mathematical and General

The effects of a magnetic field in an integrable Heisenberg chain with mixed spins

Marcio Jose Martins

Published Dec 21, 1993• 20 citations
Publisher

Abstract

We discuss some properties of an integrable and conformally invariant Heisenberg chain with alternating spins S and S' (S'>S) in the presence of a magnetic field. The zero-field magnetic susceptibility is computed and turns out to be only dependent on the spin S. For small enough magnetic field, the low-lying excitations are related to the deformed SU(2) parafermionic field theory at levels 2S and 2(S'-S). Generalizations to these results for other mixed systems are commented on.

DOI
10.1088/0305-4470/26/24/008

Related papers

Magnetic and Critical Properties of Alternating Spin Heisenberg Chain in a Magnetic Field

Tetsuji Kuramoto

We study magnetic and critical properties of the alternating spin antiferromagnetic Heisenberg chain with $S=1/2$ and 1 in a magnetic field at T=0. The numerical diagonalization is applied to the system up to $2N=20$ sites. Checking numerically that magnetic states with the magnetization per site $m$ obey a conformal field theory with conformal anomaly $c=1$ for $1/4

arXiv:cond-mat/9710229•Journal of the Physical Society of Japan•May 15, 1998•43 citations

Excitation spectra of generalized antiferromagnetic Heisenberg spin chains (abstract)

John B. Parkinson, J. C. Bonner

We compare the excitation spectra in the presence of a magnetic field of a number of integrable (exactly solvable) and nonintegrable quantum spin chains of various spin value s. The archetypal Bethe-ansatz integrable model is the s= 1/2 Heisenberg antiferromagnet (HB AFM). The excitation spectra are characterized by a soft mode which tracks across the Brillouin zone as the field increases to its saturation value. A class of Bethe-ansatz integrable models with SU(2) symmetry and the general spin s display excitation spectra qualitatively similar to the spin- 1/2 model above, for all s. A second class of Bethe-ansatz integrable models has SU(n) symmetry, where n=2s+1. Like the SU(2) integrable chains, these models have gapless excitation spectra, but the basic Brillouin zone changes from k=±2π/(2s+1)a. Studies show that periodicity of the SU(3) member of the class changes (increases) as the field increases to saturation. For both classes of integrable models, there is a single type of excitation pattern which is generically similar for all s. In the case of the other models, on the other hand, numerical studies show that the excitations divide into at least two distinct classes. In the case of the s=1 HB AFM, at high fields (corresponding to SzT=N,N−1, . . .,N/2) the excitations map approximately onto the complete set of excitations for s= 1/2 , whereas at low fields (SzT=N/2,N/2−1,. . .,0) the excitations have notable classical character. In the case of the s=1 model with pure biquadratic exchange, one set of excitations, corresponding to SzT even (SzT=N,N−2,. . .,2,0), again shows an approximate mapping to the complete excitation set for s= 1/2 . The second class of excitations, corresponding to SzT odd, are very different. They are symmetric about k=±π/2a for all SzT, i.e., correspond to a basic Brillouin zone of ±π/2a.

Journal of Applied Physics•Apr 15, 1988•0 citations

Exact S matrices for integrable quantum spin chains

Luca Mezincescu, Rafael I. Nepomechie

We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which generalizes these results. We first consider an integrable alternating spin 1/2 - spin 1 chain. In addition to having excitations with spin 1/2, this model also has excitations with spin 0. We compute the bulk S matrix, which has some unusual features. We then consider the open antiferromagnetic spin 1/2 Heisenberg chain with boundary magnetic fields. We give a direct calculation of the boundary S matrix. (Talk presented at the conference on Statistical Mechanics and Quantum Field Theory at USC, 16 - 21 May 1994)

arXiv:hep-th/9501109•Jan 24, 1995•2 citations

Thermodynamics of integrable chains with alternating spins

Hector J. de Vega, Luca Mezincescu, Rafael I. Nepomechie

We consider a two-parameter (c\ifmmode\bar\else\textasciimacron\fi{},c\ifmmode \tilde{}\else \~{}\fi{}) family of quantum integrable isotropic Hamiltonians for a chain of alternating spins of spin s=1/2 and s=1. We determine the thermodynamics for low-temperature T and small external magnetic field H, with T\ensuremath{\ll}H. In the antiferromagnetic (c\ifmmode\bar\else\textasciimacron\fi{}>0,c\ifmmode \tilde{}\else \~{}\fi{}>0) case, the model has two gapless excitations. In particular, for c\ifmmode\bar\else\textasciimacron\fi{}=c\ifmmode \tilde{}\else \~{}\fi{}, the model is conformally invariant and has central charge ${\mathit{c}}_{\mathrm{vir}}$=2. When one of these parameters is zero, the Bethe ansatz equations admit an infinite number of solutions with lowest energy.

arXiv:hep-th/9303043•Physical review. B, Condensed matter•May 1, 1994•66 citations

Critical Behaviour of Mixed Heisenberg Chains

F. C. Alcaraz, A. L. Malvezzi

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S ′) SU(2) operator interacting with a XXZ like interaction (anisotropy ∆). Our results indicate universal properties for all these chains. The whole phase, 1> ∆> −1, where the models change from ferromagnetic ( ∆ = 1) to ferrimagnetic ( ∆ = −1) behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions. 1

•Jan 1, 1996•28 citations

Critical behaviour of mixed Heisenberg chains

F C Alcaraz, A L Malvezzi

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centres are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centred in the mixed Heisenberg chain where we have at even (odd) sites a spin- SU(2) operator interacting with a XXZ-like interaction (anisotropy ). Our results indicate universal properties for all these chains. The whole phase, , where the models change from ferromagnetic to ferrimagnetic behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions.

arXiv:cond-mat/9611227•Journal of Physics A Mathematical and General•Feb 7, 1997•60 citations
We discuss some properties of an integrable and conformally invariant Heisenberg chain with alternating spins S and S' (S'>S) in the presence of a magnetic field. The zero-field magnetic susceptibility is computed and turns out to be only dependent on the spin S. For small enough magnetic field, the low-lying excitations are related to the deformed SU(2) parafermionic field theory at levels 2S and 2(S'-S). Generalizations to these results for other mixed systems are commented on.
We study magnetic and critical properties of the alternating spin antiferromagnetic Heisenberg chain with S=1/2S=1/2S=1/2 and 1 in a magnetic field at T=0. The numerical diagonalization is applied to the system up to 2N=202N=202N=20 sites. Checking numerically that magnetic states with the magnetization per site mmm obey a conformal field theory with conformal anomaly c=1c=1c=1 for $1/4
We compare the excitation spectra in the presence of a magnetic field of a number of integrable (exactly solvable) and nonintegrable quantum spin chains of various spin value s. The archetypal Bethe-ansatz integrable model is the s= 1/2 Heisenberg antiferromagnet (HB AFM). The excitation spectra are characterized by a soft mode which tracks across the Brillouin zone as the field increases to its saturation value. A class of Bethe-ansatz integrable models with SU(2) symmetry and the general spin s display excitation spectra qualitatively similar to the spin- 1/2 model above, for all s. A second class of Bethe-ansatz integrable models has SU(n) symmetry, where n=2s+1. Like the SU(2) integrable chains, these models have gapless excitation spectra, but the basic Brillouin zone changes from k=±2π/(2s+1)a. Studies show that periodicity of the SU(3) member of the class changes (increases) as the field increases to saturation. For both classes of integrable models, there is a single type of excitation pattern which is generically similar for all s. In the case of the other models, on the other hand, numerical studies show that the excitations divide into at least two distinct classes. In the case of the s=1 HB AFM, at high fields (corresponding to SzT=N,N−1, . . .,N/2) the excitations map approximately onto the complete set of excitations for s= 1/2 , whereas at low fields (SzT=N/2,N/2−1,. . .,0) the excitations have notable classical character. In the case of the s=1 model with pure biquadratic exchange, one set of excitations, corresponding to SzT even (SzT=N,N−2,. . .,2,0), again shows an approximate mapping to the complete excitation set for s= 1/2 . The second class of excitations, corresponding to SzT odd, are very different. They are symmetric about k=±π/2a for all SzT, i.e., correspond to a basic Brillouin zone of ±π/2a.
We begin with a review of the antiferromagnetic spin 1/2 Heisenberg chain. In particular, we show that the model has particle-like excitations with spin 1/2, and we compute the exact bulk S matrix. We then review our recent work which generalizes these results. We first consider an integrable alternating spin 1/2 - spin 1 chain. In addition to having excitations with spin 1/2, this model also has excitations with spin 0. We compute the bulk S matrix, which has some unusual features. We then consider the open antiferromagnetic spin 1/2 Heisenberg chain with boundary magnetic fields. We give a direct calculation of the boundary S matrix. (Talk presented at the conference on Statistical Mechanics and Quantum Field Theory at USC, 16 - 21 May 1994)
We consider a two-parameter (c\ifmmode\bar\else\textasciimacron\fi{},c\ifmmode \tilde{}\else \~{}\fi{}) family of quantum integrable isotropic Hamiltonians for a chain of alternating spins of spin s=1/2 and s=1. We determine the thermodynamics for low-temperature T and small external magnetic field H, with T\ensuremath{\ll}H. In the antiferromagnetic (c\ifmmode\bar\else\textasciimacron\fi{}>0,c\ifmmode \tilde{}\else \~{}\fi{}>0) case, the model has two gapless excitations. In particular, for c\ifmmode\bar\else\textasciimacron\fi{}=c\ifmmode \tilde{}\else \~{}\fi{}, the model is conformally invariant and has central charge cvir{\mathit{c}}_{\mathrm{vir}}cvir​=2. When one of these parameters is zero, the Bethe ansatz equations admit an infinite number of solutions with lowest energy.
The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S ′) SU(2) operator interacting with a XXZ like interaction (anisotropy ∆). Our results indicate universal properties for all these chains. The whole phase, 1> ∆> −1, where the models change from ferromagnetic ( ∆ = 1) to ferrimagnetic ( ∆ = −1) behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions. 1
The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centres are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centred in the mixed Heisenberg chain where we have at even (odd) sites a spin- SU(2) operator interacting with a XXZ-like interaction (anisotropy ). Our results indicate universal properties for all these chains. The whole phase, , where the models change from ferromagnetic to ferrimagnetic behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions.