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

Linear Antiferromagnetic Chain

Th.W. Ruijgrok, S. Rodríguez

Published Jul 15, 1960• 36 citations
Publisher

Abstract

The properties of the low-lying states of the antiferromagnetic chain are studies by means of a variational method. A trial wave function is exhibited which has an energy very close to that of the correct ground state and which displays a long-range order.
DOI
10.1103/physrev.119.596

Related papers

ON THE LINEAR ANTIFERROMAGNETIC CHAIN. Technical Report No. 20

Th.W. Ruijgrok, S. Rodríguez

The properties of the low-lying states of the antiferromagnetic chain are studied by means of a variational method. A trial wave function is exhibited which has an energy very close to that of the correct ground state and which displays a long-range order. (auth)

•Feb 1, 1960•0 citations

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

Ground-state of the linear anisotropic antiferromagnetic Heisenberg chain with nearest and next-nearest neighbor interactions

Jay D. Mancini, Janice D. Prie, William J. Massano

Solid State Communications•Feb 1, 1994•4 citations

Ground‐State Properties of Finite Antiferromagnetic Chains

H. P. van de Braak, W.J. Caspers

Abstract Exact calculations are presented for the ground state of linear antiferromagnetic Heisenberg chains with open ends. The wave function and the energy are given for chains with N = 4, 6, and 8, and quantum number S = 1/2. It is shown that in the limit for N → ∞ the ground state is probably nondegenerate and the long‐range order tends to zero. The short‐range order shows a strongly oscillating character due to end effects persisting over relatively long distances. A comparison with closed rings is made and the connection with the observation of a reduction of the zero‐point deviation in the neighbourhood of non‐magnetic impurities in more‐dimensional systems is pointed out.

physica status solidi (b)•Jan 1, 1969•1 citation

Ground state of an antiferromagnetic isotropic linear chain

Alvaro Caramico D’Auria, L. De Cesare, Ugo Esposito

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento•Aug 1, 1977•4 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
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
Abstract Exact calculations are presented for the ground state of linear antiferromagnetic Heisenberg chains with open ends. The wave function and the energy are given for chains with N = 4, 6, and 8, and quantum number S = 1/2. It is shown that in the limit for N → ∞ the ground state is probably nondegenerate and the long‐range order tends to zero. The short‐range order shows a strongly oscillating character due to end effects persisting over relatively long distances. A comparison with closed rings is made and the connection with the observation of a reduction of the zero‐point deviation in the neighbourhood of non‐magnetic impurities in more‐dimensional systems is pointed out.
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.