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

Nearest-neighbor resonating-valence-bond state in two dimensions

M. D. Johnson, K. R. Subbaswamy

Published Jun 1, 1988• 13 citations
Publisher

Abstract

The ground state of the spin-\textonehalf{} Heisenberg model with antiferromagnetic coupling on a square lattice is analyzed in terms of nearest-neighbor resonating pair-bond states. Extrapolating from finite lattice calculations it is found that the pair-bond state provides a much closer variational estimate of the ground-state energy than the widely used Gutzwiller wave function. The effect of an orthorhombic distortion of the square lattice, such as that observed in the Cu-O planes in the high-${T}_{c}$ oxides, on the spin state is analyzed by exact calculation for finite lattices. From total-energy considerations it is found that the system has a slight tendency towards such a lattice distortion.

DOI
10.1103/physrevb.37.9390

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

Resonating-valence-bond state: Comments on the antiferromagnetic ordering of the two-dimensional Heisenberg model

Mahito Kohmoto

We consider a resonating-valence-bond state as a trial wave function for the ground state of the antiferromagnetic Heisenberg model on the square lattice. The energy and the staggered spin-spin correlation functions are calculated on a small lattice and are compared with the results of the exact diagonalization of Oitmaa and Betts. The trial energy is only about 4.7% different from the exact ground-state energy on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The importance of the singlet pairs between the next-nearest antiferromagnetic sites is inferred. An argument against the previous interpretation of the numerical data as being evidence of long-range order is presented.

Physical review. B, Condensed matter•Mar 1, 1988•44 citations

RVB States for Tow-Dimensional Antiferromagnets

Makoto Inoue, Tetsuhiko Chikyu, Xiao Hu +1 more

The ground states of the antiferromagnetic Heisenberg model on the triangular and square lattices are discussed with use of the combinatorial method on the basis of Anderson's RVB (resonating-valence-bond) variational wave-function. Some properties of RVB states are studied systematically for finite system-size N up to 20 and are compared to the exact values. For the triangular lattice the estimated energy value E RVB =-2.08 is closer to the exact value than that of the spin-wave theory. The value E RVB =-2.36 is estimated for the square lattice. For the square lattice our RVB state is closer to the exact ground state than the Néel state is in the sense of a wave-function. The dimer problem has a close relation to RVB states and is used to count exactly the number of singlet-pair configurations.

Journal of the Physical Society of Japan•Nov 15, 1988•11 citations

A Variational Approach to Understanding the Ground State of a Square-Lattice Heisenberg Antiferromagnet

Shin-ichi Nakagawa, Takehiko Hamada, Jun-ichi Kane +1 more

The trial function including a few variational parameters introduced by the consideration of geometrical characters is proposed for the purpose of discussing the exact ground-state wave function of spin-1/2 Heisenberg antiferromagnet on a square lattice. In this wave function, the essential contribution of singlet pairings with larger separations between spin sites rather than the 1st nearest neighbor is taken into account. The obtained solution for spin number N ≤26 on the basis of this extended RVB (resonating-valence-bond) picture comes quite close to the exact solution, though we use only a few geometrical parameters for the systems constituted by many degrees of freedom.

Journal of the Physical Society of Japan•Apr 15, 1990•8 citations

Resonating-valence-bond theory for the square-planar lattice

Daniel Klein, Thomas G. Schmalz, M. A. Garcriaaa-Bach +2 more

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Physical review. B, Condensed matter•Jan 1, 1991•13 citations

Some New Variational Resonating-Valence-Bond-Type Wave Functions for the Spin-½ Antiferromagnetic Heisenberg Model on a Square Lattice

S. Liang, Benoît Douçot, P. W. Anderson

We consider a class of singlet resonanting-valence-bond wave functions on a square lattice, with the bond-length distribution as a variational parameter. This class contains the two limiting cases of the dimer wave function and of the N\'eel state. We present numerical calculations of the energy and the spin-spin correlation functions up to very large lattice sizes (180\ifmmode\times\else\texttimes\fi{}180) both for disordered states with exponentially decaying correlation functions and for ordered states. The energy of a disordered state can be within 0.1% of our best ordered state ($\frac{\ensuremath{-}0.3344J}{\mathrm{bond}}$).

Physical Review Letters•Jul 18, 1988•519 citations
The ground state of the spin-\textonehalf{} Heisenberg model with antiferromagnetic coupling on a square lattice is analyzed in terms of nearest-neighbor resonating pair-bond states. Extrapolating from finite lattice calculations it is found that the pair-bond state provides a much closer variational estimate of the ground-state energy than the widely used Gutzwiller wave function. The effect of an orthorhombic distortion of the square lattice, such as that observed in the Cu-O planes in the high-Tc{T}_{c}Tc​ oxides, on the spin state is analyzed by exact calculation for finite lattices. From total-energy considerations it is found that the system has a slight tendency towards such a lattice distortion.
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 consider a resonating-valence-bond state as a trial wave function for the ground state of the antiferromagnetic Heisenberg model on the square lattice. The energy and the staggered spin-spin correlation functions are calculated on a small lattice and are compared with the results of the exact diagonalization of Oitmaa and Betts. The trial energy is only about 4.7% different from the exact ground-state energy on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The importance of the singlet pairs between the next-nearest antiferromagnetic sites is inferred. An argument against the previous interpretation of the numerical data as being evidence of long-range order is presented.
The ground states of the antiferromagnetic Heisenberg model on the triangular and square lattices are discussed with use of the combinatorial method on the basis of Anderson's RVB (resonating-valence-bond) variational wave-function. Some properties of RVB states are studied systematically for finite system-size N up to 20 and are compared to the exact values. For the triangular lattice the estimated energy value E RVB =-2.08 is closer to the exact value than that of the spin-wave theory. The value E RVB =-2.36 is estimated for the square lattice. For the square lattice our RVB state is closer to the exact ground state than the Néel state is in the sense of a wave-function. The dimer problem has a close relation to RVB states and is used to count exactly the number of singlet-pair configurations.
The trial function including a few variational parameters introduced by the consideration of geometrical characters is proposed for the purpose of discussing the exact ground-state wave function of spin-1/2 Heisenberg antiferromagnet on a square lattice. In this wave function, the essential contribution of singlet pairings with larger separations between spin sites rather than the 1st nearest neighbor is taken into account. The obtained solution for spin number N ≤26 on the basis of this extended RVB (resonating-valence-bond) picture comes quite close to the exact solution, though we use only a few geometrical parameters for the systems constituted by many degrees of freedom.
We consider a class of singlet resonanting-valence-bond wave functions on a square lattice, with the bond-length distribution as a variational parameter. This class contains the two limiting cases of the dimer wave function and of the N\'eel state. We present numerical calculations of the energy and the spin-spin correlation functions up to very large lattice sizes (180\ifmmode\times\else\texttimes\fi{}180) both for disordered states with exponentially decaying correlation functions and for ordered states. The energy of a disordered state can be within 0.1% of our best ordered state ($\frac{\ensuremath{-}0.3344J}{\mathrm{bond}}$).