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 Letters

Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-(1/2 antiferromagnetic Heisenberg chain with 1/ r 2 exchange

F. D. M. Haldane

Published Feb 15, 1988• 836 citations
Publisher

Abstract

A set of Jastrow wave functions comprises exact eigenstates of a family of S= $\frac{1}{2}$ antiferromagnetic chains with ${\mathrm{r}}^{\mathrm{\ensuremath{-}}2}$ exchange. The ground state of the isotropic model is in this set, and is identical to the U\ensuremath{\rightarrow}\ensuremath{\infty} limit of the Gutzwiller wave function, also identified as Anderson's ``resonating-valence-bond'' state. The full set of energy levels of this model is obtained; the spectrum exhibits remarkable ``supermultiplet'' degeneracies suggesting the existence of a hidden continuous symmetry.

DOI
10.1103/physrevlett.60.635

Related papers

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

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

New Paired-Wavefunction for the Frustrated Antiferromagnetic Spin-Half Chain

Zou Ha

I propose a new paired-wavefunction with a parameter that continuously interpolates from the 1D Jastrow-product to the Majumdar-Ghosh dimer-wavefunction appropriate for the frustrated Heisenberg $S = 1/2$ antiferromagnet. This spin paired-state constructed in $S_z$ basis is an alternative to the well-known resonating-valence-bond basis state for describing the $S = 0$ ground-state with no apparent long-range spin order. Some numerical evidences are presented.

arXiv:cond-mat/9712015•Dec 1, 1997•0 citations

Bond operator theory of isotropic spin-1 antiferromagnetic chains

Hanting Wang, Jue-Lian Shen, Zhao-Bin Su

The bond operator representation of quantum $S=\frac{1}{2}$ spins with the singlet state being projected out is applied to investigate the isotropic spin-1 Heisenberg antiferromagnetic chain $H={\ensuremath{\sum}}_{i}[{\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}\ensuremath{-}\ensuremath{\beta}({\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}{)}^{2}]$. In the approximation of Bose condensation, the ground-state properties of the system and their $\ensuremath{\beta}$ dependences are studied. The results at Heisenberg point $\ensuremath{\beta}=0$ and at valence-bond-solid (VBS) point $\ensuremath{\beta}=\ensuremath{-}\frac{1}{3}$ agree quite well with the analytical, numerical, and experimental studies. The excitation spectrum is nonsymmetric with respect to $k=\ensuremath{\pi}/2$ and shows a minimum at $k=\ensuremath{\pi}$. The $\ensuremath{\beta}$ dependences of the ground-state energy and the excitation gap show the similarities between the Heisenberg point and VBS point. The related properties of the spin ladders are also discussed.

Physical review. B, Condensed matter•Dec 1, 1997•29 citations

Ground state of the two-dimensional antiferromagnetic Heisenberg model and the resonating-valence-bond states

Sanyee Tang, H. Q. Lin

We have studied the relation between the resonating-valence-bond (RVB) state and the exact ground state for the two-dimensional antiferromagnetic (AF) Heisenberg model on a few small lattices. We describe a method to obtain the state of minimum energy within a family of RVB states. Based on the insight provided by the RVB states, and supported by our numerical results, we argue in favor of the existence of long-range order at T=0 for the two-dimensional AF Heisenberg model.

Physical review. B, Condensed matter•Oct 1, 1988•22 citations

Spin-Liquid Ground State in a Two-Dimensional Nonfrustrated Spin Model

Giuseppe E. Santoro, Sandro Sorella, Leonardo Guidoni +2 more

We consider an exchange model describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on the square lattice. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit, and is known to show a spin-Peierls-like dimerization in one dimension. In two dimensions we calculate energy gaps, susceptibilities, and correlation functions with a Green's function Monte Carlo method. We find a finite triplet and singlet gap, with no evidence of order of any kind. We conclude that the ground state is, most likely, a spin liquid of resonating valence bonds.

arXiv:cond-mat/9902116•Physical Review Letters•Oct 11, 1999•39 citations
A set of Jastrow wave functions comprises exact eigenstates of a family of S= 12\frac{1}{2}21​ antiferromagnetic chains with r\ensuremath−2{\mathrm{r}}^{\mathrm{\ensuremath{-}}2}r\ensuremath−2 exchange. The ground state of the isotropic model is in this set, and is identical to the U\ensuremath{\rightarrow}\ensuremath{\infty} limit of the Gutzwiller wave function, also identified as Anderson's resonating-valence-bond'' state. The full set of energy levels of this model is obtained; the spectrum exhibits remarkable supermultiplet'' degeneracies suggesting the existence of a hidden continuous symmetry.
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.
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.
I propose a new paired-wavefunction with a parameter that continuously interpolates from the 1D Jastrow-product to the Majumdar-Ghosh dimer-wavefunction appropriate for the frustrated Heisenberg S=1/2S = 1/2S=1/2 antiferromagnet. This spin paired-state constructed in SzS_zSz​ basis is an alternative to the well-known resonating-valence-bond basis state for describing the S=0S = 0S=0 ground-state with no apparent long-range spin order. Some numerical evidences are presented.
The bond operator representation of quantum S=12S=\frac{1}{2}S=21​ spins with the singlet state being projected out is applied to investigate the isotropic spin-1 Heisenberg antiferromagnetic chain $H={\ensuremath{\sum}}_{i}[{\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}\ensuremath{-}\ensuremath{\beta}({\mathbf{S}}_{i}\ensuremath{\cdot}{\mathbf{S}}_{i+1}{)}^{2}]$. In the approximation of Bose condensation, the ground-state properties of the system and their $\ensuremath{\beta}$ dependences are studied. The results at Heisenberg point $\ensuremath{\beta}=0$ and at valence-bond-solid (VBS) point $\ensuremath{\beta}=\ensuremath{-}\frac{1}{3}$ agree quite well with the analytical, numerical, and experimental studies. The excitation spectrum is nonsymmetric with respect to $k=\ensuremath{\pi}/2$ and shows a minimum at $k=\ensuremath{\pi}$. The $\ensuremath{\beta}$ dependences of the ground-state energy and the excitation gap show the similarities between the Heisenberg point and VBS point. The related properties of the spin ladders are also discussed.
We consider an exchange model describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on the square lattice. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit, and is known to show a spin-Peierls-like dimerization in one dimension. In two dimensions we calculate energy gaps, susceptibilities, and correlation functions with a Green's function Monte Carlo method. We find a finite triplet and singlet gap, with no evidence of order of any kind. We conclude that the ground state is, most likely, a spin liquid of resonating valence bonds.