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

Physical review. B, Condensed matter

Coherent states as solutions of the anisotropic Heisenberg antiferromagnetic chain

Miguel Lagos, G. G. Cabrera

Published Jul 1, 1988• 24 citations
Publisher

Abstract

We propose a coherent-state solution for the one-dimensional antiferromagnetic Heisenberg Hamiltonian in the quasi-Ising asymptotic regime. We discuss the nature of the spectrum and the eigenvectors as a function of the anisotropy parameter. Results for the energy of the ground state and the short-range-order correlation agree with exact numerical calculations in a wide range of variation of anisotropy. We also present a canonical formulation of the theory which interpolates continuously from the Ising limit to cases of lower anisotropies, thus yielding a novel view of antiferromagnetism. Finally we discuss possible connections with the theory of superconductivity of high-${T}_{c}$ ceramics.

DOI
10.1103/physrevb.38.659

Related papers

NEW SOLUTIONS FOR THE ANISOTROPIC ANTIFERROMAGNETIC CHAIN

Miguel Lagos, G. G. Cabrera

Coherent states are proposed as solutions for the antiferromagnetic Heisenberg Hamiltonian in the quasi-Ising asymptotic regime of high anisotropy. Since our solutions are given in closed analytical form, a deep insight concerning the structure of the ground state and its excitations is obtained. Our calculation is in excellent agreement with numerical simulations.

Le Journal de Physique Colloques•Dec 1, 1988•0 citations

Linear Antiferromagnetic Chain with Anisotropic Coupling

R. Orbach

The exact solution is given for a linear chain of $N$ atoms of spin \textonehalf{} coupled together by the anisotropic Hamiltonian $\mathcal{H}=2J\ensuremath{\Sigma}\stackrel{N}{i=1}[{{S}_{i}}^{z}{{S}_{i+1}}^{z}+(1\ensuremath{-}\ensuremath{\alpha})({{S}_{i}}^{x}{{S}_{i+1}}^{x}+{{S}_{i}}^{y}{{S}_{i+1}}^{y})].$ The energy of the antiferromagnetic ground state is computed and comparison is made with a variational method. The parameter $\ensuremath{\alpha}$ is allowed to vary between 0 and 1, regulating the relative amount of Ising anisotropy. The short-range order, $\ensuremath{\Sigma}{i}^{}{{S}_{i}}^{z}{{S}_{i+1}}^{z}$, is calculated exactly from the variation of the ground-state energy with $\ensuremath{\alpha}$. It is shown that a kink in the short-range order curve calculated using the variational method is fictitious, and the associated discontinuity in $\frac{{\ensuremath{\partial}}^{2}E}{\ensuremath{\partial}{\ensuremath{\alpha}}^{2}}$ is nonexistent. A discussion is given of long-range order and criticisms are presented regarding the predictions of the variational method.

Physical Review•Oct 15, 1958•532 citations

Order-disorder quantum phase transition in the quasi-one-dimensional spin-1/2 collinear antiferromagnetic Heisenberg model

S. Rufo, Griffith Mendonça, J. A. Plascak +1 more

The ground-state properties of the quasi-one-dimensional spin-$1/2$ antiferromagnetic Heisenberg model is investigated by using a variational method. Spins on chains along the $x$ direction are antiferromagnetically coupled with exchange $J>0$, while spins between chains in the $y$ direction are coupled either ferromagnetically (${J}^{\ensuremath{'}}<0$) or antiferromagnetically (${J}^{\ensuremath{'}}>0$). The staggered and the colinear antiferromagnetic magnetizations are computed and their dependence on the anisotropy parameter $\ensuremath{\lambda}=|{J}^{\ensuremath{'}}|/J$ is analyzed. It is found that an infinitesimal interchain coupling parameter is sufficient to stabilize a long-range order with either a staggered magnetization ${m}_{s}$ (${J}^{\ensuremath{'}}>0$) or a colinear antiferromagnetic magnetization ${m}_{caf}$ (${J}^{\ensuremath{'}}<0$), both behaving as $\ensuremath{\simeq}{\ensuremath{\lambda}}^{1/2}$ for $\ensuremath{\lambda}\ensuremath{\rightarrow}0$.

Physical Review E•Sep 20, 2013•6 citations

Excitations for the one-dimensional S = 1 pseudo-Heisenberg antiferromagnetic chain

E. V. Orlenko, Fedor E. Orlenko, George G. Zegrya

We are interested in the anisotropic S=1 antiferromagnetic chain. System of particles with an arbitrary spin is described directly from the first principles, based on the symmetry law. The ground state of the one-dimensional S=1 pseudo-Heisenberg antiferromagnet with single-ion anisotropy is calculated. Excitations of the chain in the form of nonlinear spin waves and, in particular, the possibility of a soliton solution is considered.

Natural Science•Jan 1, 2010•1 citation

A nove1 approach to antiferromagnetism in low dimensional syst ems

G. G. Cabrera, Gleb Wataghin

We develop a theory for antiferromagnetism which is asymp- totically exact in the limit of high correlation. A trial ground state wave function is obtained through a bosonization of the Heisenberg Hamiltonian in the axial-anisotropy region. This state is represented as a quantum CO- herent state displaying long-range order. Quantities of physical interest are calculated in closed analytic form and compared with exact results or numerical simulations, showing an excellent agreement in a wide range of variation of the anisotropy parameter. We discuss the limitations of our theory near the isotropic point

•Jan 1, 1991•0 citations

Low-temperature thermodynamic properties of a random anisotropic antiferromagnetic chain

J. E. Hirsch

The low-temperature thermodynamic properties of a spin-\textonehalf{} one-dimensional random anisotropic (Heisenberg-Ising) antiferromagnet described by the Hamiltonian $H=\ensuremath{\Sigma}{i}^{}{J}_{i}({\ensuremath{\sigma}}_{x}^{i}{\ensuremath{\sigma}}_{x}^{i+1}+{\ensuremath{\sigma}}_{y}^{i}{\ensuremath{\sigma}}_{y}^{i+1}+\ensuremath{\gamma}{\ensuremath{\sigma}}_{z}^{i}{\ensuremath{\sigma}}_{z}^{i+1})$ are studied as a function of disorder and anisotropy. The ${J}_{i}>~0$ are independent random variables obeying a probability distribution $P(J)$, and $0<~\ensuremath{\gamma}<~\ensuremath{\infty}$. The approach used is a numerical implementation of a real-space renormalization-group (RG) method previously introduced. The isotropic Heisenberg case ($\ensuremath{\gamma}=1$), the $\mathrm{XY}$ case ($\ensuremath{\gamma}=0$). and the Ising case ($\ensuremath{\gamma}=\ensuremath{\infty}$) are fixed points of the RG transformation. It is found that in the $\mathrm{XY}$ region $\ensuremath{\gamma}<~1$, including the Heisenberg point, the system exhibits singular behavior in the thermodynamic properties for arbitrary probability distributions for the couplings. For the $\mathrm{XY}$ limit ($\ensuremath{\gamma}=0$) this is in agreement with known exact results. The functional form for the low-temperature susceptibility is found to be $\ensuremath{\chi}\ensuremath{\sim}\frac{1}{(T{\mathrm{ln}}^{m}(\frac{T}{{T}_{0}}))}$ in the entire region $0<~\ensuremath{\gamma}<~1$ for arbitrary probability distributions. In the Ising region ($\ensuremath{\gamma}>1$) the susceptibility shows an approximate power-law divergence for small anisotropy but goes eventually to zero as $T\ensuremath{\rightarrow}0$. Possible relevance of these results to recent experiments on Qn${(\mathrm{TCNQ})}_{2}$ is discussed.

Physical review. B, Condensed matter•Dec 1, 1980•48 citations
We propose a coherent-state solution for the one-dimensional antiferromagnetic Heisenberg Hamiltonian in the quasi-Ising asymptotic regime. We discuss the nature of the spectrum and the eigenvectors as a function of the anisotropy parameter. Results for the energy of the ground state and the short-range-order correlation agree with exact numerical calculations in a wide range of variation of anisotropy. We also present a canonical formulation of the theory which interpolates continuously from the Ising limit to cases of lower anisotropies, thus yielding a novel view of antiferromagnetism. Finally we discuss possible connections with the theory of superconductivity of high-Tc{T}_{c}Tc​ ceramics.
The exact solution is given for a linear chain of NNN atoms of spin \textonehalf{} coupled together by the anisotropic Hamiltonian $\mathcal{H}=2J\ensuremath{\Sigma}\stackrel{N}{i=1}[{{S}_{i}}^{z}{{S}_{i+1}}^{z}+(1\ensuremath{-}\ensuremath{\alpha})({{S}_{i}}^{x}{{S}_{i+1}}^{x}+{{S}_{i}}^{y}{{S}_{i+1}}^{y})].$ The energy of the antiferromagnetic ground state is computed and comparison is made with a variational method. The parameter $\ensuremath{\alpha}$ is allowed to vary between 0 and 1, regulating the relative amount of Ising anisotropy. The short-range order, $\ensuremath{\Sigma}{i}^{}{{S}_{i}}^{z}{{S}_{i+1}}^{z}$, is calculated exactly from the variation of the ground-state energy with $\ensuremath{\alpha}$. It is shown that a kink in the short-range order curve calculated using the variational method is fictitious, and the associated discontinuity in $\frac{{\ensuremath{\partial}}^{2}E}{\ensuremath{\partial}{\ensuremath{\alpha}}^{2}}$ is nonexistent. A discussion is given of long-range order and criticisms are presented regarding the predictions of the variational method.
The ground-state properties of the quasi-one-dimensional spin-1/21/21/2 antiferromagnetic Heisenberg model is investigated by using a variational method. Spins on chains along the xxx direction are antiferromagnetically coupled with exchange J>0J>0J>0, while spins between chains in the yyy direction are coupled either ferromagnetically (${J}^{\ensuremath{'}}<0$) or antiferromagnetically (${J}^{\ensuremath{'}}>0$). The staggered and the colinear antiferromagnetic magnetizations are computed and their dependence on the anisotropy parameter $\ensuremath{\lambda}=|{J}^{\ensuremath{'}}|/J$ is analyzed. It is found that an infinitesimal interchain coupling parameter is sufficient to stabilize a long-range order with either a staggered magnetization ms{m}_{s}ms​ (${J}^{\ensuremath{'}}>0$) or a colinear antiferromagnetic magnetization mcaf{m}_{caf}mcaf​ (${J}^{\ensuremath{'}}<0$), both behaving as $\ensuremath{\simeq}{\ensuremath{\lambda}}^{1/2}$ for $\ensuremath{\lambda}\ensuremath{\rightarrow}0$.
We develop a theory for antiferromagnetism which is asymp- totically exact in the limit of high correlation. A trial ground state wave function is obtained through a bosonization of the Heisenberg Hamiltonian in the axial-anisotropy region. This state is represented as a quantum CO- herent state displaying long-range order. Quantities of physical interest are calculated in closed analytic form and compared with exact results or numerical simulations, showing an excellent agreement in a wide range of variation of the anisotropy parameter. We discuss the limitations of our theory near the isotropic point
The low-temperature thermodynamic properties of a spin-\textonehalf{} one-dimensional random anisotropic (Heisenberg-Ising) antiferromagnet described by the Hamiltonian $H=\ensuremath{\Sigma}{i}^{}{J}_{i}({\ensuremath{\sigma}}_{x}^{i}{\ensuremath{\sigma}}_{x}^{i+1}+{\ensuremath{\sigma}}_{y}^{i}{\ensuremath{\sigma}}_{y}^{i+1}+\ensuremath{\gamma}{\ensuremath{\sigma}}_{z}^{i}{\ensuremath{\sigma}}_{z}^{i+1})$ are studied as a function of disorder and anisotropy. The Ji> 0{J}_{i}>~0Ji​> 0 are independent random variables obeying a probability distribution P(J)P(J)P(J), and $0<~\ensuremath{\gamma}<~\ensuremath{\infty}$. The approach used is a numerical implementation of a real-space renormalization-group (RG) method previously introduced. The isotropic Heisenberg case ($\ensuremath{\gamma}=1$), the XY\mathrm{XY}XY case ($\ensuremath{\gamma}=0$). and the Ising case ($\ensuremath{\gamma}=\ensuremath{\infty}$) are fixed points of the RG transformation. It is found that in the XY\mathrm{XY}XY region $\ensuremath{\gamma}<~1$, including the Heisenberg point, the system exhibits singular behavior in the thermodynamic properties for arbitrary probability distributions for the couplings. For the XY\mathrm{XY}XY limit ($\ensuremath{\gamma}=0$) this is in agreement with known exact results. The functional form for the low-temperature susceptibility is found to be $\ensuremath{\chi}\ensuremath{\sim}\frac{1}{(T{\mathrm{ln}}^{m}(\frac{T}{{T}_{0}}))}$ in the entire region $0<~\ensuremath{\gamma}<~1$ for arbitrary probability distributions. In the Ising region ($\ensuremath{\gamma}>1$) the susceptibility shows an approximate power-law divergence for small anisotropy but goes eventually to zero as $T\ensuremath{\rightarrow}0$. Possible relevance of these results to recent experiments on Qn(TCNQ)2{(\mathrm{TCNQ})}_{2}(TCNQ)2​ is discussed.