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

Annalen der Physik

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

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

Published Jan 1, 1993• 8 citations
Publisher

Abstract

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.

DOI
10.1002/andp.19935050105

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

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

George Jackeli, Japaridze, G

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.

•Jan 17, 1996•2 citations

Electrons with correlated hopping interaction in one dimension

G. I. Japaridze, E. Müller‐Hartmann

Abstract The 1D system of correlated electrons characterized in addition to the usual on‐site (U) and nearest‐neighbour (V) repulsion by a correlated‐hopping term (t*) is considered. The ground state phase diagram is studied within the framework of the weak‐coupling continuum‐limit approach. At filling v the effective interaction originating from the correlated‐hopping term which appears in the continuum‐limit theory is given by t* cos (πv). Being repulsive for v < 1/2 and attractive for v > 1/2, this interaction leads to a characteristic band‐filling dependence of the phase diagram of the system. For v ≠ 1/2, depending on the relation between the bare values of the coupling constants (U, V, t* cos (π v)) and, hence, on the band‐filling, the system shows three different phases in the infrared limit: a Luttinger metal, a nonmagnetic metal and a singlet superconducting phase. For v = 1/2, the correlated‐hopping interaction is dynamically trivial, leading only to a renormalization of the oneelectron hopping amplitude and the phase diagram of the model coincides with that of the extended Hubbard model.

Annalen der Physik•Jan 1, 1994•35 citations

Insulating phases driven by unequal on-site repulsion in the 1D unconventional Hubbard model

Yan Xu, Hanqin Ding, Jun Zhang

The one-dimensional unconventional Hubbard model with alternating on-site interaction at odd (Uo) and even (Ue) lattice sites is analytically studied in the weak-coupling regime. The existence of unequal on-site repulsion (Uo≠Ue) makes a dramatic impact on the charge excitation behavior in one dimension. At quarter filling, the alternating Hubbard interaction leads to the occurrence of umklapp processes and to the generation of a charge gap. As usual, the low-energy spin excitation is still massless. The ground state shows insulating behavior, characterized by the coexisting spin-density-wave and charge-density-wave instabilities.

Results in Physics•Apr 22, 2021•2 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

The metal-insulator transition in one dimension

Heinz J. Schulz

The low--energy excited states of a system of interacting one--dimensional fermions in a conducting state are collective charge and spin density oscillations. The unusual physical properties of such a system (called ``Luttinger liquid'') are characterized by the velocities $u_ρ$ and $u_σ$ of the charge and spin excitations, as well as by a parameter $K_ρ$ that determines the power law behavior of correlation functions. Umklapp scattering occuring at half--filling or other commensurate bandfilling can lead to a transition into an insulating state, characterized in particular by a gap in the charge excitations (the Mott--Hubbard gap). The properties in the vicinity of the transition are shown to depend on both the way the transition is approached (constant bandfilling and varying interaction, or constant interaction and varying bandfilling) and on the ``order'' of the commensurability. In particular, even and odd fractional fillings show quite different behavior. This behavior is illustrated in detail using lattice models like the Hubbard model and its extensions.

arXiv:cond-mat/9412036•Dec 7, 1994•7 citations
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 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.
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.
Abstract The 1D system of correlated electrons characterized in addition to the usual on‐site (U) and nearest‐neighbour (V) repulsion by a correlated‐hopping term (t*) is considered. The ground state phase diagram is studied within the framework of the weak‐coupling continuum‐limit approach. At filling v the effective interaction originating from the correlated‐hopping term which appears in the continuum‐limit theory is given by t* cos (πv). Being repulsive for v < 1/2 and attractive for v > 1/2, this interaction leads to a characteristic band‐filling dependence of the phase diagram of the system. For v ≠ 1/2, depending on the relation between the bare values of the coupling constants (U, V, t* cos (π v)) and, hence, on the band‐filling, the system shows three different phases in the infrared limit: a Luttinger metal, a nonmagnetic metal and a singlet superconducting phase. For v = 1/2, the correlated‐hopping interaction is dynamically trivial, leading only to a renormalization of the oneelectron hopping amplitude and the phase diagram of the model coincides with that of the extended Hubbard model.
The one-dimensional unconventional Hubbard model with alternating on-site interaction at odd (Uo) and even (Ue) lattice sites is analytically studied in the weak-coupling regime. The existence of unequal on-site repulsion (Uo≠Ue) makes a dramatic impact on the charge excitation behavior in one dimension. At quarter filling, the alternating Hubbard interaction leads to the occurrence of umklapp processes and to the generation of a charge gap. As usual, the low-energy spin excitation is still massless. The ground state shows insulating behavior, characterized by the coexisting spin-density-wave and charge-density-wave instabilities.
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.
The low--energy excited states of a system of interacting one--dimensional fermions in a conducting state are collective charge and spin density oscillations. The unusual physical properties of such a system (called ``Luttinger liquid'') are characterized by the velocities uρu_ρuρ​ and uσu_σuσ​ of the charge and spin excitations, as well as by a parameter KρK_ρKρ​ that determines the power law behavior of correlation functions. Umklapp scattering occuring at half--filling or other commensurate bandfilling can lead to a transition into an insulating state, characterized in particular by a gap in the charge excitations (the Mott--Hubbard gap). The properties in the vicinity of the transition are shown to depend on both the way the transition is approached (constant bandfilling and varying interaction, or constant interaction and varying bandfilling) and on the ``order'' of the commensurability. In particular, even and odd fractional fillings show quite different behavior. This behavior is illustrated in detail using lattice models like the Hubbard model and its extensions.