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

International Journal of Modern Physics B

ORBITAL CORRELATIONS IN SPINLESS HUBBARD CHAIN

Chatchai Srinitiwarawong, Pongpun Punpet

Published Jun 30, 2008• 0 citations
Publisher

Abstract

We have calculated the orbital correlation of the spinless two orbitals Hubbard chain in the limit of a very strong on-site Coulomb interaction and half-filling. The Hamiltonian is written in the form of pseudospin operators, and the Hilbert space is restricted to those states with only one electron per lattice site. The ground state wave function has been calculated using the density matrix renormalization group method. It has been found that the orbital correlations occur in the chain along the x-, y-, and z-axis and these are in antiferro-orbital states.

DOI
10.1142/s0217979208039691

Related papers

Ground state of E[subscript g] electron in the spinless hubbard model

Pongpun Punpet, Chatchai Srinitiwarawong

The ground-state properties of a simple model for transition metal oxide compounds in ferromagnetic phase have been studied. This model only contains the orbital degree of freedom. The two-orbital spinless Hubbard model in the limit of strong on-site coulomb interaction (U) has been used to describe the motion of election in e[subscript g] orbital. In the large-U and half-filling limits, the effective Hamilto-nian has been derived from the Hubbard model by the canonical transformation. After the transformation, the doubly occupied states have been projected out and the size of the Hillbert space has been reduced. For this effective Hamiltonian, the hopping amplitudes have been defined according to the managanite system which consists of three axes: x-, y- and z-axis. Since the ground-state properties of the effective Hamiltonian have been calculated only in one-dimension, then the results of this work have been separated in three cases; the electrons hopping in x, y, and z axes respectively. The ground-state wavefunction of this effective Hamiltionian has been calculated by infinite density matrix renormalization group algorithm. This algorithm leads to the ground state at the thermodynamic limit when the number of sties is large. It has been found that the ground-state energies are equivalent in all hopping axes. Furthermore, the nearest neighbor orbital correlations at the ground state for all axes are antiferro-orbital.

•Jan 1, 2005•0 citations

Perturbation theory of the Hubbard Hamiltonian on a 4×4 cluster of the square lattice

J. Galán, José Antonio Vergés

The ground-state wave function and energy are calculated for the one-band Hubbard Hamiltonian on a 4\ifmmode\times\else\texttimes\fi{}4 cluster of the square lattice up to first and second order of the on-site Coulomb repulsion U, respectively. Changes induced by a deviation of the number of electrons from half-filling (one electron per lattice site) are closely followed. Charge-charge and spin-spin correlation functions are directly obtained from the ground-state wave function and show the existence of antiferromagnetic correlations that extend over the whole cluster at half-filling. Correlations among sites separated by more than a lattice site diminish very rapidly as holes are introduced into the cluster. The analysis is extended to the negative-U case. Ground-state properties change qualitatively.

Physical review. B, Condensed matter•Nov 1, 1991•13 citations

Phase diagram of the two-chain Hubbard model

Young‐Ho Park, Shoudan Liang, T. K. Lee

We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.

arXiv:cond-mat/9811280•Physical review. B, Condensed matter•Jan 15, 1999•11 citations

The half-filled Hubbard chain in the Composite Operator Method: A comparison with Bethe Ansatz

M. M. Sánchez, A. Avella, F. Mancini

PACS. 71.10.−w – Theories and models of many electron systems. PACS. 71.10.Fd – Lattice fermion models. PACS. 71.15.Th – Other methods. Abstract. – The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model

•Jan 1, 1998•8 citations

Correlations in an extended Hubbard model with Ising-like interaction

Robertson C. Esperanza, Francis N. C. Paraan

Density-density and spin-spin correlations are calculated in an extended Hubbard model with an intersite Ising-like interaction. Local expectation values and correlation functions involving charge density and magnetization are obtained using the density matrix renormalization group (DMRG) for a periodic chain of L = 10 sites at half-filling. Antiferromagnetic phases with spin and charge density modulation are identified and located in a phase diagram.

Proceedings of the Samahang Pisika ng Pilipinas•May 13, 2017•0 citations

Quarter-Filled Extended Hubbard Model at Strong Coupling

W. F. Lee, Hua Lin

We apply a perturbation approach to study the quarter-filled extended Hubbard model at strong coupling limit. An effective Hamiltonian up to sixth order in t/U and t/V (t defines electron hopping, U defines on-site Coulomb interaction, and V defines nearest-neighbor Coulomb interaction) for one-dimensional chains was obtained. The spin-spin correlation functions were involved, which can be obtained after comparing to the ground state energy numerically obtained from the phase diagram.

International Journal of Modern Physics B•Aug 10, 2003•1 citation
We have calculated the orbital correlation of the spinless two orbitals Hubbard chain in the limit of a very strong on-site Coulomb interaction and half-filling. The Hamiltonian is written in the form of pseudospin operators, and the Hilbert space is restricted to those states with only one electron per lattice site. The ground state wave function has been calculated using the density matrix renormalization group method. It has been found that the orbital correlations occur in the chain along the x-, y-, and z-axis and these are in antiferro-orbital states.
The ground-state properties of a simple model for transition metal oxide compounds in ferromagnetic phase have been studied. This model only contains the orbital degree of freedom. The two-orbital spinless Hubbard model in the limit of strong on-site coulomb interaction (U) has been used to describe the motion of election in e[subscript g] orbital. In the large-U and half-filling limits, the effective Hamilto-nian has been derived from the Hubbard model by the canonical transformation. After the transformation, the doubly occupied states have been projected out and the size of the Hillbert space has been reduced. For this effective Hamiltonian, the hopping amplitudes have been defined according to the managanite system which consists of three axes: x-, y- and z-axis. Since the ground-state properties of the effective Hamiltonian have been calculated only in one-dimension, then the results of this work have been separated in three cases; the electrons hopping in x, y, and z axes respectively. The ground-state wavefunction of this effective Hamiltionian has been calculated by infinite density matrix renormalization group algorithm. This algorithm leads to the ground state at the thermodynamic limit when the number of sties is large. It has been found that the ground-state energies are equivalent in all hopping axes. Furthermore, the nearest neighbor orbital correlations at the ground state for all axes are antiferro-orbital.
The ground-state wave function and energy are calculated for the one-band Hubbard Hamiltonian on a 4\ifmmode\times\else\texttimes\fi{}4 cluster of the square lattice up to first and second order of the on-site Coulomb repulsion U, respectively. Changes induced by a deviation of the number of electrons from half-filling (one electron per lattice site) are closely followed. Charge-charge and spin-spin correlation functions are directly obtained from the ground-state wave function and show the existence of antiferromagnetic correlations that extend over the whole cluster at half-filling. Correlations among sites separated by more than a lattice site diminish very rapidly as holes are introduced into the cluster. The analysis is extended to the negative-U case. Ground-state properties change qualitatively.
We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.
PACS. 71.10.−w – Theories and models of many electron systems. PACS. 71.10.Fd – Lattice fermion models. PACS. 71.15.Th – Other methods. Abstract. – The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropriate framework for the half-filled Hubbard chain and can be applied to evaluate properties, like the correlation functions, which cannot be obtained by means of the Bethe Ansatz, except for some limiting cases. Introduction. – New materials whose physics is dominated by electron correlations in narrow energy bands are actually a challenge for solid state physicists. The treatment of such systems is not trivial due to the competition between itinerant and localized behaviour of the electrons in these bands. The Hubbard Hamiltonian [1] is regarded as the simplest model