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

Spin Jastrow state

Tao Pang

Published Feb 1, 1991• 6 citations
Publisher

Abstract

A variational ansatz with quantum fluctuations at all ranges is introduced to describe the ground state of the antiferromagnetic Heisenberg model. As an example, the ground-state energy and staggered magnetization of the spin-1/2 square lattice are evaluated from the variational principle. The form of the short-range correlation factor in the ansatz for this system is obtained. The properties of the ground state are then analyzed based on these findings.

DOI
10.1103/physrevb.43.3362

Related papers

Variational calculation for the spin-(1/2 Heisenberg antiferromagnet on a square lattice

Chandan Dasgupta

The ground-state properties of the spin-(1/2 Heisenberg antiferromagnet on a square lattice are studied by using a simple variational wave function that interpolates continuously between the N\'eel state and short-range resonating-valence-bond states. Exact calculations of the variational energy for small systems show that the state with the lowest energy has long-range antiferromagnetic order. The staggered magnetization in this state is approximately 70% of its maximum possible value. The variational estimate of the ground-state energy is substantially lower than the value obtained for the nearest-neighbor resonating-valence-bond wave function.

Physical review. B, Condensed matter•Jan 1, 1989•10 citations

A New Variational Ansatz for the Ground State of the 2 d -Heisenberg Antiferromagnet

Claudio Albanese, Christoph Bruder

We propose a new variational ansatz for the ground state of the (isotropic) antiferromagnetic Heisenberg model on the square lattice. Our motivation for considering this ansatz is that the ground state of the anisotropic Heisenberg model with small transversal coupling has precisely this form. The evaluation of the expectation value of the energy is reduced to the problem of measuring the statistical expectation value of a certain correlation function of an Ising model on the square lattice itself. Hence we can deal with this problem by using a Monte Carlo method.

Europhysics Letters (EPL)•Mar 1, 1989•0 citations

The ground state of two quantum models of magnetism

J. Oitmaa, Donald D. Betts

The ground state energy and pair correlations have been computed exactly for the spin [Formula: see text] XY magnet and isotropic Heisenberg antiferromagnet, for a sequence of finite cells on the square and honeycomb lattices. Precise estimates of the ground state energy of the infinite lattices are obtained by extrapolation. It is predicted that the XY magnet has a non-zero transverse magnetization and the Heisenberg antiferromagnet has a non-zero staggered magnetization in the ground state.

Canadian Journal of Physics•Jul 1, 1978•353 citations

Ground-state properties of the two-dimensional antiferromagnetic Heisenberg model

Mark Gross, Eduardo Sánchez-Velasco, Eric D. Siggia

The ground-state energy, staggered magnetization, and correlation function are computed for the two-dimensional spin-(1/2 quantum antiferromagnetic Heisenberg model (believed to be relevant to the high-temperature superconducting materials without doping) on lattices up to 24\ifmmode\times\else\texttimes\fi{}24 by Monte Carlo methods extrapolated to zero temperature. A more accurate value for the ground-state energy is determined by the method of Neumann and Ulam by extrapolating from lattices up to 12\ifmmode\times\else\texttimes\fi{}12.

Physical review. B, Condensed matter•Feb 1, 1989•113 citations

Exact diagonalization of finite frustrated spin-(1/2 Heisenberg models

Francisco E. Figueirido, A. Karlhede, Steven Allan Kivelson +3 more

We have studied the spectrum of low-spin eigenstates of a spin-(1/2 Heisenberg model on 4\ifmmode\times\else\texttimes\fi{}4 square lattices with up to third-neighbor antiferromagnetic exchange interactions. We have computed the staggered susceptibility, spin-spin correlation function, and the overlap of the exact ground state with various variational spin-density-wave ordered states as well as with the equal-amplitude, nearest-neighbor resonating-valence-bond state (which is the prototypical short-ranged RVB state). We find evidence for a complicated phase diagram with a region in which a short-ranged RVB state may be the ground state.

Physical review. B, Condensed matter•Mar 1, 1990•137 citations

Improved variational wave function for the two-dimensional spin-1/2 Heisenberg antiferromagnet

C. E. I. Carneiro, Xiangyu Kong, Robert H. Swendsen

We present a variational wave function for the ground state of the two-dimensional spin-1/2 Heisenberg antiferromagnet. It is a modification of a Monte Carlo variational wave function proposed by Huse and Elser which gives excellent results for the ground-state energy but breaks the rotational symmetry of the squared staggered magnetization. In their case the x component of the squared staggered magnetization (${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{2}$ is much larger than (${\mathit{m}}_{\mathit{y}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{2}$ and (${\mathit{m}}_{\mathit{z}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{2}$, which are the y and z components, respectively. In this paper we show how to restore the symmetry between ${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ and ${\mathit{m}}_{\mathit{y}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. However, ${\mathit{m}}_{\mathit{z}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ is still much smaller than ${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. We also study the enforcement of the full rotational symmetry in our trial wave function using only two spin interaction terms. Finally, we discuss how errors in Monte Carlo data affect the efficiency of algorithms which determine more systematically the best variational parameters for the ground-state wave function.

Physical review. B, Condensed matter•Feb 1, 1994•5 citations
A variational ansatz with quantum fluctuations at all ranges is introduced to describe the ground state of the antiferromagnetic Heisenberg model. As an example, the ground-state energy and staggered magnetization of the spin-1/2 square lattice are evaluated from the variational principle. The form of the short-range correlation factor in the ansatz for this system is obtained. The properties of the ground state are then analyzed based on these findings.
The ground-state properties of the spin-(1/2 Heisenberg antiferromagnet on a square lattice are studied by using a simple variational wave function that interpolates continuously between the N\'eel state and short-range resonating-valence-bond states. Exact calculations of the variational energy for small systems show that the state with the lowest energy has long-range antiferromagnetic order. The staggered magnetization in this state is approximately 70% of its maximum possible value. The variational estimate of the ground-state energy is substantially lower than the value obtained for the nearest-neighbor resonating-valence-bond wave function.
We propose a new variational ansatz for the ground state of the (isotropic) antiferromagnetic Heisenberg model on the square lattice. Our motivation for considering this ansatz is that the ground state of the anisotropic Heisenberg model with small transversal coupling has precisely this form. The evaluation of the expectation value of the energy is reduced to the problem of measuring the statistical expectation value of a certain correlation function of an Ising model on the square lattice itself. Hence we can deal with this problem by using a Monte Carlo method.
The ground-state energy, staggered magnetization, and correlation function are computed for the two-dimensional spin-(1/2 quantum antiferromagnetic Heisenberg model (believed to be relevant to the high-temperature superconducting materials without doping) on lattices up to 24\ifmmode\times\else\texttimes\fi{}24 by Monte Carlo methods extrapolated to zero temperature. A more accurate value for the ground-state energy is determined by the method of Neumann and Ulam by extrapolating from lattices up to 12\ifmmode\times\else\texttimes\fi{}12.
We have studied the spectrum of low-spin eigenstates of a spin-(1/2 Heisenberg model on 4\ifmmode\times\else\texttimes\fi{}4 square lattices with up to third-neighbor antiferromagnetic exchange interactions. We have computed the staggered susceptibility, spin-spin correlation function, and the overlap of the exact ground state with various variational spin-density-wave ordered states as well as with the equal-amplitude, nearest-neighbor resonating-valence-bond state (which is the prototypical short-ranged RVB state). We find evidence for a complicated phase diagram with a region in which a short-ranged RVB state may be the ground state.
We present a variational wave function for the ground state of the two-dimensional spin-1/2 Heisenberg antiferromagnet. It is a modification of a Monte Carlo variational wave function proposed by Huse and Elser which gives excellent results for the ground-state energy but breaks the rotational symmetry of the squared staggered magnetization. In their case the x component of the squared staggered magnetization (${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$)2{)}^{2})2 is much larger than (${\mathit{m}}_{\mathit{y}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$)2{)}^{2})2 and (${\mathit{m}}_{\mathit{z}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$)2{)}^{2})2, which are the y and z components, respectively. In this paper we show how to restore the symmetry between ${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ and ${\mathit{m}}_{\mathit{y}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. However, ${\mathit{m}}_{\mathit{z}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ is still much smaller than ${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. We also study the enforcement of the full rotational symmetry in our trial wave function using only two spin interaction terms. Finally, we discuss how errors in Monte Carlo data affect the efficiency of algorithms which determine more systematically the best variational parameters for the ground-state wave function.