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

arXiv:cond-mat/0111426 · Physical Review Letters

High Spin Systems with Orbital Degeneracy

Shun-Qing Shen, X. C. Xie, Fu‐Chun Zhang

Published Dec 26, 2001• 21 citations
arXivHTMLPDF

Abstract

High-spin systems with orbital degeneracy are studied in the large spin limit. In the absence of Hund's coupling, the classical spin model is mapped onto disconnected orbital systems with spins up and down, respectively. The ground state of the isotropic model is an orbital valence bond state where each bond is an orbital singlet with parallel spins, and neighboring bonds interact antiferromagnetically. Possible relevance to the transition metal oxides is discussed.

DOI
10.1103/physrevlett.88.027201

Related papers

Generalized valence bond state and solvable models for spin- 12 systems with orbital degeneracy

Shun-Qing Shen

A spin-$\frac{1}{2}$ system with double orbital degeneracy may possess SU(4) symmetry. According to the group theory a global SU(4) singlet state can be expressed as a linear combination of all possible configurations consisting of four-site SU(4) singlets. Following Andersion's idea for spin-$\frac{1}{2}$ system, we propose that the ground state for the antiferromagnetic SU(4) model is an SU(4)-resonating valence-bond (RVB) state. A short-range SU(4)-RVB state is a spin and orbital liquid, and its elementary excitations has an energy gap. We construct a series of solvable models that ground states are short-range SU(4)-RVB states. The results are generalized to the antiferromagnetic SU(N) models.

arXiv:cond-mat/0105130•Physical review. B, Condensed matter•Sep 12, 2001•11 citations

SU(4) Theory for Spin Systems with Orbital Degeneracy

You‐Quan Li, Michael Ma, D. N. Shi +1 more

The isotropic limit of spin systems with orbital degeneracy has global SU(4) symmetry. On many 2D lattices, the ground state does not possess long-range order, which may explain the observed spin liquid properties of ${\mathrm{LiNiO}}_{2}$. In the SU(4) N\'eel-ordered state, spin-spin correlations can be antiferromagnetic between two neighboring sites with parallel magnetic moments.

arXiv:cond-mat/9804157•Physical Review Letters•Oct 19, 1998•270 citations

Exact Ground States in Spin Systems with Orbital Degeneracy

Kazuhito Itoh

We present exact ground states in spin models with orbital generacy in one and higher dimensions. A method to obtain the exact ground states of the models when the Hamiltonians are composed of the products of two commutable operators is proposed. For the case of the spin-1/2 model with two-fold degeneracy some exact ground states are given, such as the Valence-Bond (VB), the magnetically ordered, and the orbitally ordered states under particular parameter regimes. We also find the models with the higher spin and degeneracy which have the new types of VB ground states in the spin and the orbital sectors.

arXiv:cond-mat/9902238•Journal of the Physical Society of Japan•Feb 15, 1999•14 citations

Dimer phases in quantum antiferromagnets with orbital degeneracy

George Jackeli, Dmitri A. Ivanov

We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have a directional character and are represented by static Potts-like variables. In the limit of vanishing Hund's coupling, the ground-state manifold of such a model is spanned by the hard-core dimer (spin singlet) coverings of the lattice. The extensive degeneracy of dimer coverings is lifted at a finite Hund's coupling through an order--out-of-disorder mechanism by virtual triplet excitations. The relevance of our results to several experimentally studied systems is discussed.

arXiv:0705.2990•Physical Review B•Oct 22, 2007•28 citations

Spin gap in low-dimensional Mott insulators with orbital degeneracy

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

We consider the exchanged Hamiltonian HST=−J∑〈rr′〉(2Sr⋅Sr′−12)(2Tr⋅Tr′−12), describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on equivalent bonds. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit. To investigate the ground state properties we use a Green’s Function Monte Carlo, calculating energy gaps and correlation functions, the latter through the forward walking technique. In one dimension we find that the ground state is a “crystal” of valence bond dimers. In two dimensions, the spin gap appears to remain finite in the thermodynamic limit, and, consistently, the staggered magnetization—signal of Néel long range order—seems to vanish. From the analysis of dimer–dimer correlation functions, however, we find no sign of a valance bond crystal. A spin liquid appears as a plausible scenario compatible with our findings.

arXiv:cond-mat/9809013•Journal of Applied Physics•Apr 15, 1999•1 citation

Alternating Spin and Orbital Dimerization and Spin-Gap Formation in Coupled Spin-Orbital Systems

Swapan Kumar Pati, Rajiv R. P. Singh, Daniel I. Khomskii

We discuss a novel mechanism for obtaining a spin-gap state through the creation of a coherent spin-orbital structure in systems with orbital degeneracy. Using the density matrix renormalization group, we calculate the phase diagram for a coupled spin-orbital model. We find that, in addition to ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The relevance to several recently discovered materials is discussed.

arXiv:cond-mat/9807270•Physical Review Letters•Dec 14, 1998•131 citations
High-spin systems with orbital degeneracy are studied in the large spin limit. In the absence of Hund's coupling, the classical spin model is mapped onto disconnected orbital systems with spins up and down, respectively. The ground state of the isotropic model is an orbital valence bond state where each bond is an orbital singlet with parallel spins, and neighboring bonds interact antiferromagnetically. Possible relevance to the transition metal oxides is discussed.
A spin-12\frac{1}{2}21​ system with double orbital degeneracy may possess SU(4) symmetry. According to the group theory a global SU(4) singlet state can be expressed as a linear combination of all possible configurations consisting of four-site SU(4) singlets. Following Andersion's idea for spin-12\frac{1}{2}21​ system, we propose that the ground state for the antiferromagnetic SU(4) model is an SU(4)-resonating valence-bond (RVB) state. A short-range SU(4)-RVB state is a spin and orbital liquid, and its elementary excitations has an energy gap. We construct a series of solvable models that ground states are short-range SU(4)-RVB states. The results are generalized to the antiferromagnetic SU(N) models.
The isotropic limit of spin systems with orbital degeneracy has global SU(4) symmetry. On many 2D lattices, the ground state does not possess long-range order, which may explain the observed spin liquid properties of LiNiO2{\mathrm{LiNiO}}_{2}LiNiO2​. In the SU(4) N\'eel-ordered state, spin-spin correlations can be antiferromagnetic between two neighboring sites with parallel magnetic moments.
We present exact ground states in spin models with orbital generacy in one and higher dimensions. A method to obtain the exact ground states of the models when the Hamiltonians are composed of the products of two commutable operators is proposed. For the case of the spin-1/2 model with two-fold degeneracy some exact ground states are given, such as the Valence-Bond (VB), the magnetically ordered, and the orbitally ordered states under particular parameter regimes. We also find the models with the higher spin and degeneracy which have the new types of VB ground states in the spin and the orbital sectors.
We study and solve the ground-state problem of a microscopic model for a family of orbitally degenerate quantum magnets. The orbital degrees of freedom are assumed to have a directional character and are represented by static Potts-like variables. In the limit of vanishing Hund's coupling, the ground-state manifold of such a model is spanned by the hard-core dimer (spin singlet) coverings of the lattice. The extensive degeneracy of dimer coverings is lifted at a finite Hund's coupling through an order--out-of-disorder mechanism by virtual triplet excitations. The relevance of our results to several experimentally studied systems is discussed.
We consider the exchanged Hamiltonian HST=−J∑〈rr′〉(2Sr⋅Sr′−12)(2Tr⋅Tr′−12), describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on equivalent bonds. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in the large Hubbard repulsion limit. To investigate the ground state properties we use a Green’s Function Monte Carlo, calculating energy gaps and correlation functions, the latter through the forward walking technique. In one dimension we find that the ground state is a “crystal” of valence bond dimers. In two dimensions, the spin gap appears to remain finite in the thermodynamic limit, and, consistently, the staggered magnetization—signal of Néel long range order—seems to vanish. From the analysis of dimer–dimer correlation functions, however, we find no sign of a valance bond crystal. A spin liquid appears as a plausible scenario compatible with our findings.
We discuss a novel mechanism for obtaining a spin-gap state through the creation of a coherent spin-orbital structure in systems with orbital degeneracy. Using the density matrix renormalization group, we calculate the phase diagram for a coupled spin-orbital model. We find that, in addition to ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The relevance to several recently discovered materials is discussed.