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/0405048 · Journal of Physics Condensed Matter

Effective Hamiltonian for a half-filled Hubbard chain with alternating on-site interactions

Paata Kakashvili, George I Japaridze

Published Aug 3, 2004• 8 citations
arXivHTMLPDF

Abstract

We derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin $S=1/2$ Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange.

DOI
10.1088/0953-8984/16/32/017

Related papers

Effective Hamiltonian for a Half-filled Hubbard Chain with Alternating On-site Interactions

Paata Kakashvili, G. I. Japaridze

We derive an effective spin Hamiltonian for the one-dimensional half-filled alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin S = 1/2 Heisenberg chain with asymmetric next-nearest-neighbour (nnn) exchange.

•Jan 1, 2004•5 citations

Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

I. Grusha, M. Z. Menteshashvili, G. I. Japaridze

We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model (IHM) with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin S = 1/2 anisotropic XXZ Heisenberg chain with alternating next-nearest-neighbor (NNN) and three-spin couplings in the presence of a uniform and a staggered magnetic field.

arXiv:1506.06109•International Journal of Modern Physics B•Jan 6, 2016•6 citations

Effective Hamiltonian for a half-filled tetramerized ionic-Hubbard chain

M. Z. Menteshashvili, N.D. Chachava, G. I. Japaridze

We derive an effective spin Hamiltonian for the one-dimensional half-filled tetramerized ionic-Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian which describes the low-energy spin sector of the model is a spin S=1/2 Heisenberg Hamiltonian with alternating nearest-neighbour exchange.

arXiv:0801.1290•Jan 8, 2008•0 citations

Phase diagram of the half-filled Hubbard chain with next-nearest-neighbor hopping

S. Daul, R. M. Noack

We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the density-matrix renormalization-group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion U, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U, sufficiently large next-nearest-neighbor hopping ${t}_{2}$ leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.

arXiv:cond-mat/9907256•Physical review. B, Condensed matter•Jan 15, 2000•53 citations

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

Jean-Yves P. Delannoy, Michel J. P. Gingras, P. C. W. Holdsworth +1 more

We investigate the ground state properties of the two-dimensional half-filled one band Hubbard model in the strong (large-$U$) to intermediate coupling limit (i.e., away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order $t{(t∕U)}^{3}$. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as $t∕U$ is increased from the $t∕U\ensuremath{\rightarrow}0$ Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an $S=1∕2$ antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of $t∕U$, despite the fact that the moment of the spin Hamiltonian, which depends on transverse spin fluctuations only, in an increasing function of $t∕U$. We also comment on quantitative aspects of the $t∕U$ and $1∕S$ expansions.

arXiv:cond-mat/0412033•Physical Review B•Sep 16, 2005•53 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 derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin S=1/2S=1/2S=1/2 Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange.
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the density-matrix renormalization-group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion U, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U, sufficiently large next-nearest-neighbor hopping t2{t}_{2}t2​ leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.
We investigate the ground state properties of the two-dimensional half-filled one band Hubbard model in the strong (large-UUU) to intermediate coupling limit (i.e., away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t∕U)3t{(t∕U)}^{3}t(t∕U)3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t∕Ut∕Ut∕U is increased from the $t∕U\ensuremath{\rightarrow}0$ Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S=1∕2S=1∕2S=1∕2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t∕Ut∕Ut∕U, despite the fact that the moment of the spin Hamiltonian, which depends on transverse spin fluctuations only, in an increasing function of t∕Ut∕Ut∕U. We also comment on quantitative aspects of the t∕Ut∕Ut∕U and 1∕S1∕S1∕S expansions.