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

Renormalization group approach to the one-dimensional 1/4-filled Hubbard model with alternating on-site interactions

George Jackeli, Japaridze, G

Published Jan 17, 1996• 2 citations
OpenAlex

Abstract

The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a gap in the charge excitation spectrum for $U_{a}\\not=U_{b}$, $U_{a}>0$ or $U_{b}>0$. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.

Related papers

Renormalization Group Approach to the One–Dimensional 1/4–Filled Hubbard Model with Alternating on–Site Interactions

George Jackeli, G. Japaridze

The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system, and to the dynamical generation of a gap in the charge excitation spectrum for Ua≠Ub, Ua>0 or Ub>0. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum, and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.

arXiv:cond-mat/9908441•International Journal of Modern Physics B•Jun 30, 1997•2 citations

The one‐dimensional 1/4‐filled Hubbard model with alternating interactions

G. I. Japaridze, Daniel I. Khomskii, E. Müller‐Hartmann

Abstract The one‐dimensional Hubbard model with different on‐site interaction on the even (Ua) and odd (Ub) sites is considered within the framework of the weak coupling approach. In the case of a 1/4‐filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for Ua ≠ Ub and Ua>0 or Ub>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next‐nearest neighbour sites is also considered.

Annalen der Physik•Jan 1, 1993•8 citations

Unequal on-site interaction effects in the one-dimensional electron system at quarter filling

Hanqin Ding, Yan Xu, Weiting Chen

The one-dimensional antiferromagnetic correlated electron system described by the unusual t-U-J model with alternating on-site interactions at odd ([Formula: see text]) and even ([Formula: see text]) sites is studied analytically. At weak coupling, the use of bosonization and renormalization-group techniques helps to obtain ground-state phase diagram. At quarter filling, the unequal on-site repulsion ([Formula: see text]) causes the occurrence of umklapp processes and the generation of a charge excitation gap. Contrary to the usual case ([Formula: see text]), the system is not metallic but insulating. For [Formula: see text], the system is in a spin-gapped phase with charge-density-wave (CDW) instability; for [Formula: see text], the system is in a spin-gapless phase characterized by the coexistence of both CDW and spin-density-wave (SDW) instabilities, where the SDW correlation dominates over the CDW one.

Scientific Reports•May 24, 2021•3 citations

Ground-state phase diagram of the unconventional Hubbard chain with bond–charge interaction

Xin Sun, Liyue Wang, Hanqin Ding

Using the field-theory approach combining bosonization and renormalization group, we investigate the weak-coupling phase diagram of the unconventional Hubbard chain, where in addition to a bond–charge interaction ( X ), the Hubbard interaction differs between odd ( U o ) and even ( U e ) sites. The result shows that at quarter filling, the unequal Hubbard repulsion has a great influence on low-energy charge excitations. For the attractive X , the umklapp scattering always exists, and the ground state only exhibits a spin-gapless insulating phase with dominant spin-density-wave correlations. For the repulsive X , the umklapp processes only take place if both U o and U e are greater than 8 X cos ( π / 4 ) , and the phase diagram consists of three phases, a metallic phase with the spin-gapped singlet superconducting correlation, and two insulating phases characterized by the spin-density-wave and charge-density-wave correlations. We also present the phase diagram of the standard t - U - X chain in the case of non-half filling. • We study the 1D modified t-U-X model with unequal on-site interaction. • The different on-site repulsion induces relevant umklapp process at quarter filling. • The study supplements understanding of quantum properties of 1D correlated systems.

Results in Physics•Aug 23, 2024•0 citations

Ground-state properties of the one-dimensional modified Penson–Kolb–Hubbard model

Yan Xu, Hanqin Ding

The ground-state properties of a 1D modified Penson–Kolb–Hubbard model characterized by alternating Hubbard interaction at odd and even sites are discussed by the bosonization scheme and the renormalization group analysis. At quarter filling, the quantum phase diagram consists of the charge-density-wave, spin-density-wave and singlet-superconductivity instabilities. The insulating phases come from the relevant umklapp process induced by the unequal on-site repulsion. The results provide a further understanding of occurrence of the umklapp process in 1D correlated electron systems.

Results in Physics•Aug 19, 2022•1 citation

Real-space renormalization-group study of the two-dimensional Hubbard model

Jesús Pérez-Conde, Pierre M. Pfeuty

The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (${\mathit{t}}_{\mathit{y}}$=${\mathit{t}}_{\mathit{x}}$); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=${\mathit{t}}_{\mathit{y}}$/${\mathit{t}}_{\mathit{x}}$, is different from the unity and zero the ground state is a conductor up to a critical value (U/t${)}_{\mathit{c}1}$, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t${)}_{\mathit{c}2}$\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.

Physical review. B, Condensed matter•Jan 1, 1993•16 citations
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a gap in the charge excitation spectrum for Uanot=UbU_{a}\\not=U_{b}Ua​not=Ub​, Ua>0U_{a}>0Ua​>0 or Ub>0U_{b}>0Ub​>0. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system, and to the dynamical generation of a gap in the charge excitation spectrum for Ua≠Ub, Ua>0 or Ub>0. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum, and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered.
Abstract The one‐dimensional Hubbard model with different on‐site interaction on the even (Ua) and odd (Ub) sites is considered within the framework of the weak coupling approach. In the case of a 1/4‐filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for Ua ≠ Ub and Ua>0 or Ub>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next‐nearest neighbour sites is also considered.
The one-dimensional antiferromagnetic correlated electron system described by the unusual t-U-J model with alternating on-site interactions at odd ([Formula: see text]) and even ([Formula: see text]) sites is studied analytically. At weak coupling, the use of bosonization and renormalization-group techniques helps to obtain ground-state phase diagram. At quarter filling, the unequal on-site repulsion ([Formula: see text]) causes the occurrence of umklapp processes and the generation of a charge excitation gap. Contrary to the usual case ([Formula: see text]), the system is not metallic but insulating. For [Formula: see text], the system is in a spin-gapped phase with charge-density-wave (CDW) instability; for [Formula: see text], the system is in a spin-gapless phase characterized by the coexistence of both CDW and spin-density-wave (SDW) instabilities, where the SDW correlation dominates over the CDW one.
Using the field-theory approach combining bosonization and renormalization group, we investigate the weak-coupling phase diagram of the unconventional Hubbard chain, where in addition to a bond–charge interaction ( X ), the Hubbard interaction differs between odd ( U o ) and even ( U e ) sites. The result shows that at quarter filling, the unequal Hubbard repulsion has a great influence on low-energy charge excitations. For the attractive X , the umklapp scattering always exists, and the ground state only exhibits a spin-gapless insulating phase with dominant spin-density-wave correlations. For the repulsive X , the umklapp processes only take place if both U o and U e are greater than 8 X cos ( π / 4 ) , and the phase diagram consists of three phases, a metallic phase with the spin-gapped singlet superconducting correlation, and two insulating phases characterized by the spin-density-wave and charge-density-wave correlations. We also present the phase diagram of the standard t - U - X chain in the case of non-half filling. • We study the 1D modified t-U-X model with unequal on-site interaction. • The different on-site repulsion induces relevant umklapp process at quarter filling. • The study supplements understanding of quantum properties of 1D correlated systems.
The ground-state properties of a 1D modified Penson–Kolb–Hubbard model characterized by alternating Hubbard interaction at odd and even sites are discussed by the bosonization scheme and the renormalization group analysis. At quarter filling, the quantum phase diagram consists of the charge-density-wave, spin-density-wave and singlet-superconductivity instabilities. The insulating phases come from the relevant umklapp process induced by the unequal on-site repulsion. The results provide a further understanding of occurrence of the umklapp process in 1D correlated electron systems.
The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (ty{\mathit{t}}_{\mathit{y}}ty​=tx{\mathit{t}}_{\mathit{x}}tx​); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=ty{\mathit{t}}_{\mathit{y}}ty​/tx{\mathit{t}}_{\mathit{x}}tx​, is different from the unity and zero the ground state is a conductor up to a critical value (U/t)c1{)}_{\mathit{c}1})c1​, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t)c2{)}_{\mathit{c}2})c2​\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.