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

Journal of the Physical Society of Japan

Study of Spin System witht2gOrbital Degeneracy for Ladder and Chain

Nobuyuki Katoh

Published Jan 15, 1999• 5 citations
Publisher

Abstract

Effective spin Hamiltonians with t 2g orbital degeneracy have been investigated theoretically. We assume that a d electron occupies one of doubly degenerate d z x and d y z orbitals which have the lowest energy in atomic level. The orbital degrees of freedom are represented as Ising iso-spin operators because of the symmetry of the orbital characters. We apply the Hamiltonians to a ladder and a chain lattices and investigate the models using the exact diagonalization. For the ladder model, a spin gap opens above a finite value of the spin exchange coupling on rung, which is qualitatively different from the ladder model with single orbital. For the chain model, the spin gap behavior is observed in the uniform spin correlation at low temperature. Origin of the spin gap is a spin-dimer triggered by the occurrence of the ferromagnetic orbital ordering, which suggests a new mechanism of the spin gap formation.

DOI
10.1143/jpsj.68.258

Related papers

Orbital Order Effect of Two-Dimensional Spin Gap System forCaV4O9

Nobuyuki Katoh, Masatoshi Imada

Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV$_4$O$_9$ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in $d^1$ state of V, $d_{xz}$ and $d_{yz}$ orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied $d_{xy}$ orbital in addition to orbital order of partially filled $d_{xz}$ and $d_{yz}$ orbitals.

arXiv:cond-mat/9712051•Journal of the Physical Society of Japan•Feb 15, 1998•9 citations

Correlated spin and orbital dimerizations in spin-orbital models

Swapan Kumar Pati, Rajiv R. P. Singh

We study a one-dimensional spin-orbital model with Heisenberg symmetry for spins and $\mathrm{XY}$ symmetry for orbital degrees of freedom. We establish the ground-state phase diagram of this model. The gapless phases of the model consist of fully polarized ferromagnetic spin states together with the filled Jordan-Wigner Fermi sea for the orbitals. Two such phases, with ferromagnetic and antiferromagnetic $\mathrm{XY}$ correlations for the orbitals, are found. All other phases are found to have a spin gap with degenerate ground states. Two types of correlated spin and orbital dimerizations are observed: (i) spin singlet with orbital singlet in alternating rungs and (ii) spin singlet with orbital triplet in the same rung. The phase boundaries, energy gaps, and order parameters are evaluated using the density matrix renormalization group method.

Physical review. B, Condensed matter•Mar 1, 2000•14 citations

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

Singlet quantum phases of the frustrated spin-1/2 ladder with ferromagnetic (F) exchange in legs and alternating F-AF exchange in rungs

Monalisa Chatterjee, Manoranjan Kumar, Z. G. Soos

Abstract Ladders with 2 N spins-1/2 and singlet ( S = 0) ground states are studied numerically using exact diagonalization and density matrix renormalization group (DMRG) calculations. The curvatures E ″ ( s ) of states with the lowest energy E ( s ) at spin s = S / N ≤ 1 are obtained in the thermodynamic limit. All states have E ″ ( s ) > 0 in two phases, one with strong F exchange J F in rungs, the other with strong F exchange J L in legs. The Dimer phase with frustrated F exchanges has one or more states with E ″ ( s ) < 0. All three phases have finite gaps to the lowest triplet state. The ladder at J F → ∞ is adiabatically connected to the spin-1 Heisenberg AF chain, and at J L → ∞ to the J 1 − J 2 model.

Physica Scripta•Dec 22, 2023•3 citations

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains

David G. Shelton, A. A. Nersesyan, Alexei M. Tsvelik

We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains (spin ladder). It is shown that the system always has a spectral gap and the lower lying excitations are triplets. For the case of identical chains the model in the continuous limit is shown to be equivalent to four decoupled noncritical Ising models with the ${\mathit{Z}}_{2}$\ifmmode\times\else\texttimes\fi{}SU(2) symmetry. For this case we obtain the exact expressions for asymptotics of spin-spin correlation functions. It is shown that when the chains have different exchange integrals ${\mathit{J}}_{1}$\ensuremath{\gg}${\mathit{J}}_{2}$ the spectrum at low energies is described by the O(3)-nonlinear \ensuremath{\sigma} model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9508047•Physical review. B, Condensed matter•Apr 1, 1996•368 citations

Excitations in the anisotropic spin-orbital model

Jan Bała, Andrzej M. Oleś, G. A. Sawatzky

We study the elementary excitations of the ferromagnetic spin-orbital model which represents the low-energy excitations for strongly correlated electrons described by the Hubbard Hamiltonian with a twofold degeneracy. At most two and four spin-and-orbital bound states have been found in one and two dimensions, respectively. For a completely degenerate system, the spin-and-orbital bound states are the lowest-lying elementary excitations in most of the Brillouin zone and for Ising-like interactions they can have much lower energy than the other excitations of the model and might thus be responsible for the instability of the ground state. This might lead to quantum disordered states in both spin and orbital space, as indicated by exact solutions obtained for small clusters.

Physical review. B, Condensed matter•Mar 5, 2001•7 citations
Effective spin Hamiltonians with t 2g orbital degeneracy have been investigated theoretically. We assume that a d electron occupies one of doubly degenerate d z x and d y z orbitals which have the lowest energy in atomic level. The orbital degrees of freedom are represented as Ising iso-spin operators because of the symmetry of the orbital characters. We apply the Hamiltonians to a ladder and a chain lattices and investigate the models using the exact diagonalization. For the ladder model, a spin gap opens above a finite value of the spin exchange coupling on rung, which is qualitatively different from the ladder model with single orbital. For the chain model, the spin gap behavior is observed in the uniform spin correlation at low temperature. Origin of the spin gap is a spin-dimer triggered by the occurrence of the ferromagnetic orbital ordering, which suggests a new mechanism of the spin gap formation.
Effects of possible orbital order in magnetic properties of two-dimensional spin gap system for CaV4_44​O9_99​ are investigated theoretically. After analyzing experimental data, we show that single orbital models assumed in the literature are insufficient to reproduce the data. To understand the origin of the discrepancy, we assume that in d1d^1d1 state of V, dxzd_{xz}dxz​ and dyzd_{yz}dyz​ orbitals have substantial contributions in the lowest-energy atomic level which leads to a double-degeneracy. We study possible configurations of the orbital order. By exact diagonalization and perturbation expansion, we calculate the susceptibility, wavenumber dependence of low-lying excitations and equal-time spin-spin correlations which is related to integrated intensity of the neutron inelastic scattering. These quantities sensitively depend on the configuration of the orbital order. The calculated results for some configurations of the orbital order reproduce many experimental results much better than the previous single-orbital models. However some discrepancy still remains to completely reproduce all of the reported experimental results. To understand the origin of these discrepancies, we point out the possible importance of the partially occupied dxyd_{xy}dxy​ orbital in addition to orbital order of partially filled dxzd_{xz}dxz​ and dyzd_{yz}dyz​ orbitals.
We study a one-dimensional spin-orbital model with Heisenberg symmetry for spins and XY\mathrm{XY}XY symmetry for orbital degrees of freedom. We establish the ground-state phase diagram of this model. The gapless phases of the model consist of fully polarized ferromagnetic spin states together with the filled Jordan-Wigner Fermi sea for the orbitals. Two such phases, with ferromagnetic and antiferromagnetic XY\mathrm{XY}XY correlations for the orbitals, are found. All other phases are found to have a spin gap with degenerate ground states. Two types of correlated spin and orbital dimerizations are observed: (i) spin singlet with orbital singlet in alternating rungs and (ii) spin singlet with orbital triplet in the same rung. The phase boundaries, energy gaps, and order parameters are evaluated using the density matrix renormalization group method.
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.
Abstract Ladders with 2 N spins-1/2 and singlet ( S = 0) ground states are studied numerically using exact diagonalization and density matrix renormalization group (DMRG) calculations. The curvatures E ″ ( s ) of states with the lowest energy E ( s ) at spin s = S / N ≤ 1 are obtained in the thermodynamic limit. All states have E ″ ( s ) > 0 in two phases, one with strong F exchange J F in rungs, the other with strong F exchange J L in legs. The Dimer phase with frustrated F exchanges has one or more states with E ″ ( s ) < 0. All three phases have finite gaps to the lowest triplet state. The ladder at J F → ∞ is adiabatically connected to the spin-1 Heisenberg AF chain, and at J L → ∞ to the J 1 − J 2 model.
We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains (spin ladder). It is shown that the system always has a spectral gap and the lower lying excitations are triplets. For the case of identical chains the model in the continuous limit is shown to be equivalent to four decoupled noncritical Ising models with the Z2{\mathit{Z}}_{2}Z2​\ifmmode\times\else\texttimes\fi{}SU(2) symmetry. For this case we obtain the exact expressions for asymptotics of spin-spin correlation functions. It is shown that when the chains have different exchange integrals J1{\mathit{J}}_{1}J1​\ensuremath{\gg}J2{\mathit{J}}_{2}J2​ the spectrum at low energies is described by the O(3)-nonlinear \ensuremath{\sigma} model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility. \textcopyright{} 1996 The American Physical Society.
We study the elementary excitations of the ferromagnetic spin-orbital model which represents the low-energy excitations for strongly correlated electrons described by the Hubbard Hamiltonian with a twofold degeneracy. At most two and four spin-and-orbital bound states have been found in one and two dimensions, respectively. For a completely degenerate system, the spin-and-orbital bound states are the lowest-lying elementary excitations in most of the Brillouin zone and for Ising-like interactions they can have much lower energy than the other excitations of the model and might thus be responsible for the instability of the ground state. This might lead to quantum disordered states in both spin and orbital space, as indicated by exact solutions obtained for small clusters.