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Annalen der Physik

Electrons with correlated hopping interaction in one dimension

G. I. Japaridze, E. Müller‐Hartmann

Published Jan 1, 1994• 35 citations
Publisher

Abstract

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.

DOI
10.1002/andp.19945060304

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Results in Physics•Apr 24, 2023•5 citations
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.
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.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction T∗{T}^{*}T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.
By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.
A one-dimensional model of interacting electrons with on-site U, nearest- neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, \U - 2V\ < \2W\ and a bond-spin-density-wave (BSDW) for W > 0, \U - 2V\ < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the eta(pi) -superconducting phase at \U - 2V\ much less than 2t less than or equal to W is briefly discussed.
The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.
At non-half-filling, a one-dimensional interacting electronic model (t–U–R) is studied analytically. The particular correlated hopping keeps particle–hole symmetry of the Hubbard model. Physically, the model involved is equivalent to an extended Hubbard chain incorporating a two-body (X) and a three-body (X˜) site-bond interactions with X˜=2X. The analysis of weak-coupling theory leads to the ground-state phase diagram, which consists of three types of metallic phases, characterized by the charge- (CDW) and spin-density-wave (SDW) and singlet-superconductivity (SS) instabilities.