Dimerization and spin gap in strongly correlated systems

We investigate the ground-state property and the excitation gap of a one-dimensional spin-orbital model with isotropic spin and anisotropic orbital exchange interactions, which represents the strong-coupling limit of a two-orbital Hubbard model including the Hund's rule coupling $(J)$ at quarter filling, by using a density-matrix renormalization group method. At $J=0$ , spin and orbital correlations coincide with each other with a peak at $q=\ensuremath{\pi}∕2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing $J$ , the peak position of orbital correlation changes to $q=\ensuremath{\pi}$, while that of spin correlation remains at $q=\ensuremath{\pi}∕2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state.We investigate the ground-state property and the excitation gap of a one-dimensional spin-orbital model with isotropic spin and anisotropic orbital exchange interactions, which represents the strong-coupling limit of a two-orbital Hubbard model including the Hund's rule coupling $(J)$ at quarter filling, by using a density-matrix renormalization group method. At $J=0$, spin and orbital correlations coincide with each other with a peak at $q=\ensuremath{\pi}∕2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing $J$, the peak position of orbital correlation changes to $q=\ensuremath{\pi}$, while that of spin correlation remains at $q=\ensuremath{\pi}∕2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state.

arXiv:cond-mat/0701092Physical Review BJul 31, 20073 citations

Spin gap and phase separation in one-dimensional strongly correlated electron systems

Masaaki Nakamura, K. Nomura, Atsuhiro Kitazawa +3 more

Jan 1, 19980 citations

Theory of Strongly Correlated Systems

Rishabh Jha

arXiv:2507.07195Lecture notes in physicsJan 1, 20260 citations

Spin-gap state and superconducting correlations in a one-dimensional dimerizedt-Jmodel

Masatoshi Imada

The phase diagram of one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed.The phase diagram of one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed.

Physical review. B, Condensed matterJul 1, 199333 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.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/9809013Journal of Applied PhysicsApr 15, 19991 citation

New Theoretical Approaches to Strongly Correlated Systems

Springer eBooksJan 1, 200161 citations

(J)

at quarter filling, by using a density-matrix renormalization group method. At

J=0

, spin and orbital correlations coincide with each other with a peak at $q=\ensuremath{\pi}∕2$, corresponding to the SU(4) singlet state. On the other hand, spin and orbital states change in a different way due to the Hund's rule coupling. With increasing

J

, the peak position of orbital correlation changes to $q=\ensuremath{\pi}$, while that of spin correlation remains at $q=\ensuremath{\pi}∕2$. In addition, orbital dimer correlation becomes robust in comparison with spin dimer correlation, suggesting that quantum orbital fluctuation is enhanced by the Hund's rule coupling. Accordingly, a relatively large orbital gap opens in comparison with a spin gap, and the system is described by an effective spin system on the background of the orbital dimer state.