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

Zeitschrift für Physik B Condensed Matter

The valence-bond representation of the three dimensional antiferromagnetic Heisenberg model

Andreas Fledderjohann, K.-H. Mütter, P. Wielath

Published Mar 1, 1996• 2 citations
Publisher
DOI
10.1007/s002570050121

Related papers

Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

Jennifer Chayes, Lincoln Chayes, Steven Allan Kivelson

Communications in Mathematical Physics•Mar 1, 1989•58 citations

SU(N) Heisenberg model with multicolumn representations

Tsuyoshi Okubo, Kenji Harada, Jie Lou +1 more

The $\mathrm{SU}(N)$ symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the N\'eel order disappears at $N=10$, indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the N\'eel or the VBS ordering for $N\ensuremath{\ge}15$. This is actually consistent with the large-$N$ theory, which predicts that the VBS state immediately follows the N\'eel state, because the expected spontaneous order is too weak to be detected.

arXiv:1504.05332•Physical Review B•Oct 5, 2015•10 citations

Bound states in Heisenberg antiferromagnets

Stephen William Lovesey, Ewald Balcar

Physics Letters A•Sep 1, 1969•7 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

GRASSMANNIAN APPROACH TO THE RESONATING-VALENCE-BOND STATE OF THE 2D HEISENBERG ANTIFERROMAGNET

Yonathan Shapir, Thomas Blum

A systematic representation of the resonating-valence-bond state of the 2D spin-1/2 Heisenberg antiferromagnet in terms of anticommuting Grassmann variables is derived. This representation is extended to the dilute case and the holon statistics are considered. Independent phase fluctuations on each valence-bond yield a U(1) gauge theory with low-lying gapless excitations in accordance with other approaches.

Modern Physics Letters B•Aug 1, 1989•2 citations

Valence bond ground states in isotropic quantum antiferromagnets

Ian K. Affleck, Tom Kennedy, Élliott H. Lieb +1 more

Communications in Mathematical Physics•Sep 1, 1988•1,477 citations
The SU(N)\mathrm{SU}(N)SU(N) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the N\'eel order disappears at N=10N=10N=10, indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the N\'eel or the VBS ordering for $N\ensuremath{\ge}15$. This is actually consistent with the large-NNN theory, which predicts that the VBS state immediately follows the N\'eel state, because the expected spontaneous order is too weak to be detected.