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

Europhysics Letters (EPL)

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

Claudio Albanese, Christoph Bruder

Published Mar 1, 1989• 0 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/8/5/015

Related papers

Spin Jastrow state

Tao Pang

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.

Physical review. B, Condensed matter•Feb 1, 1991•6 citations

AB INITIO CALCULATIONS FOR THE SQUARE-LATTICE ANISOTROPIC HEISENBERG MODEL

R. F. Bishop, DAMIAN J. J. FARNELL

Interest in lattice quantum spin systems as models of quantum magnets has increased with the discovery of new and interesting magnetic materials. Here we use a well-known technique of quantum many-body theory, namely the coupled-cluster method (CCM), to investigate the nearest-neighbour, spin-½, anisotropic Heisenberg model on the square lattice. Ground-state expectation values for quantities such as the ground-state energy and the sublattice magnetisation are determined to an accuracy comparable with that of the best of other available techniques including Monte Carlo methods. In order to demonstrate this point we present results for various values of the anisotropy parameter, including those for the isotropic Heisenberg model and the isotropic XY model. We show that it is now possible to determine the presence and position of the quantum phase transitions using ab initio CCM calculations, and furthermore that we can accurately predict the critical behaviour at these points.

International Journal of Modern Physics B•Mar 10, 1999•0 citations

Variational calculations for the square-lattice quantum antiferromagnet

Zhiping Liu, Efstratios Manousakis

We study the spin-1/2 Heisenberg antiferromagnet on a square lattice using variational Monte Carlo calculations. We construct a variational wave function which gives accurate ground-state energy and is consistent with sum rules for the dynamical structure function. The spin-wave velocity and the spin-stiffness constant can be calculated using sum rules. We obtain ${Z}_{c}$==c/${c}_{0}$, where ${c}_{0}$ is the classical spin-wave velocity. This and other ground-state quantities are in good agreement with spin-wave theory and Monte Carlo calculations.

Physical review. B, Condensed matter•Dec 1, 1989•35 citations

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

Two-dimensional Heisenberg antiferromagnet: A numerical study

Ted Barnes, Eric S. Swanson

We describe a numerical simulation of the isotropic spin-\textonehalf{} Heisenberg antiferromagnet on square lattices of size 4\ifmmode\times\else\texttimes\fi{}4, 6\ifmmode\times\else\texttimes\fi{}6, and 8\ifmmode\times\else\texttimes\fi{}8. A Hamiltonian Monte Carlo method is used to measure the energies of the lowest-lying singlet and triplet states, and we extrapolate these results to give estimates of the properties of large antiferromagnets. Our result for the ground-state energy per spin is $\frac{{E}_{0}}{{N}^{2}}=\ensuremath{-}0.672\ifmmode\pm\else\textpm\fi{}0.001$ for an infinite system. Within our statistical accuracy, the singlet-triplet gap behaves as ${E}_{1}\ensuremath{-}{E}_{0}\ensuremath{\approx}\frac{2.1}{N}$, which implies that the infinite system is gapless.

Physical review. B, Condensed matter•Jun 1, 1988•63 citations

Variational RVB Wave Function for the Spin-1/2 Heisenberg Model on Honeycomb Lattice

Zahra Noorbakhsh, Farhad Shahbazi, S. A. Jafari +1 more

In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground state of the $S=1/2$ antiferromagnetic Heisenberg model on the honeycomb lattice. Employing Variational Monte Carlo (VMC) method, we show that the ground state energy obtained from such RVB wave function, lies well below the energy of the Néel state and compares very well to the energies evaluated from spin-wave theory and series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are different, which indicates the anisotropic nature of the system. We compare our results with the square lattice and we show that although the quantum fluctuations on honeycomb lattice are much stronger, but do not completely destroy the magnetic order.

arXiv:0812.3229•Journal of the Physical Society of Japan•Apr 27, 2009•17 citations
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.
Interest in lattice quantum spin systems as models of quantum magnets has increased with the discovery of new and interesting magnetic materials. Here we use a well-known technique of quantum many-body theory, namely the coupled-cluster method (CCM), to investigate the nearest-neighbour, spin-½, anisotropic Heisenberg model on the square lattice. Ground-state expectation values for quantities such as the ground-state energy and the sublattice magnetisation are determined to an accuracy comparable with that of the best of other available techniques including Monte Carlo methods. In order to demonstrate this point we present results for various values of the anisotropy parameter, including those for the isotropic Heisenberg model and the isotropic XY model. We show that it is now possible to determine the presence and position of the quantum phase transitions using ab initio CCM calculations, and furthermore that we can accurately predict the critical behaviour at these points.
We study the spin-1/2 Heisenberg antiferromagnet on a square lattice using variational Monte Carlo calculations. We construct a variational wave function which gives accurate ground-state energy and is consistent with sum rules for the dynamical structure function. The spin-wave velocity and the spin-stiffness constant can be calculated using sum rules. We obtain Zc{Z}_{c}Zc​==c/c0{c}_{0}c0​, where c0{c}_{0}c0​ is the classical spin-wave velocity. This and other ground-state quantities are in good agreement with spin-wave theory and Monte Carlo calculations.
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 describe a numerical simulation of the isotropic spin-\textonehalf{} Heisenberg antiferromagnet on square lattices of size 4\ifmmode\times\else\texttimes\fi{}4, 6\ifmmode\times\else\texttimes\fi{}6, and 8\ifmmode\times\else\texttimes\fi{}8. A Hamiltonian Monte Carlo method is used to measure the energies of the lowest-lying singlet and triplet states, and we extrapolate these results to give estimates of the properties of large antiferromagnets. Our result for the ground-state energy per spin is $\frac{{E}_{0}}{{N}^{2}}=\ensuremath{-}0.672\ifmmode\pm\else\textpm\fi{}0.001$ for an infinite system. Within our statistical accuracy, the singlet-triplet gap behaves as ${E}_{1}\ensuremath{-}{E}_{0}\ensuremath{\approx}\frac{2.1}{N}$, which implies that the infinite system is gapless.
In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground state of the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model on the honeycomb lattice. Employing Variational Monte Carlo (VMC) method, we show that the ground state energy obtained from such RVB wave function, lies well below the energy of the Néel state and compares very well to the energies evaluated from spin-wave theory and series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are different, which indicates the anisotropic nature of the system. We compare our results with the square lattice and we show that although the quantum fluctuations on honeycomb lattice are much stronger, but do not completely destroy the magnetic order.