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Results in Physics

Phase diagram of a generalized Penson–Kolb–Hubbard chain with the occupation-dependent hopping

Jing Xia Yu, Hanqin Ding

Published Dec 9, 2022• 2 citations
Publisher

Abstract

At half filling, we study analytically a one-dimensional correlated electronic system modeled by an extended Penson–Kolb–Hubbard (PKH) chain with the occupation-dependent hopping. The modification of the electron hopping amplitude is exhibited to induce the additional correlated-hopping interactions. At weak coupling, we use the field theory to obtain ground-state phase diagram, including the SDW, BCDW, BSDW, SS and TS phases for U>0. The induced three-body attractive interaction accounts for the superconductivity absent in the usual PKH model.

DOI
10.1016/j.rinp.2022.106169

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At half filling, we study analytically a one-dimensional correlated electronic system modeled by an extended Penson–Kolb–Hubbard (PKH) chain with the occupation-dependent hopping. The modification of the electron hopping amplitude is exhibited to induce the additional correlated-hopping interactions. At weak coupling, we use the field theory to obtain ground-state phase diagram, including the SDW, BCDW, BSDW, SS and TS phases for U>0. The induced three-body attractive interaction accounts for the superconductivity absent in the usual PKH model.
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.
By the bosonization and renormalization-group schemes, a half-filled Hubbard chain with density-dependent hopping is investigated at weak coupling. The model involved has an electron–hole symmetry and an SO(4) symmetry. The phase diagram consists of three different phases divided by a charge transition at on-site repulsion U = U c and a spin transition at U = U s , with U s = − U c = 16 π ( t c − 1 ) , including a Mott insulator with the SDW correlation, a dimerized insulator with the BCDW correlation, and a Luttinger metal with the coexisting TS and BSDW correlations. The effective three-body repulsion ( t c − 1 > 0 ) and attraction ( t c − 1 < 0 ) induce the dimerized and metallic phases, respectively. • We study a 1D Hubbard model with symmetric density-dependent hopping analytically. • We provide a theoretical scheme of realization of the BCDW and TS instabilities. • The results supplement further understanding of quantum properties of 1D correlated systems.
At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U,V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V, the attractive P may give rise to the superconducting phases for 2V≤min{2|P|;4|P|−U}.
By relaxing the conventional assumption of the equal one-electron hopping amplitude, we modify the one-dimensional half-filled Penson-Kolb (PK) model to obey the density-dependent hopping (DDH). For positive small modulation parameter [Formula: see text] and pair hopping [Formula: see text], we use bosonization and renormalization-group analysis to determine the ground state phase diagram. In the attractive case([Formula: see text]), the existence of the DDH leads to a gap transition in the spin sector and produces a fully gapless phase where a Luttinger liquid metal phase with dominant triplet superconducting correlations is realized for [Formula: see text], with the charge transition point [Formula: see text] and the spin transition point [Formula: see text]. Besides, there is a Luther-Emery matal phase with dominant singlet-superconducting correlations for [Formula: see text] and a Haldane insulator phase characterized by dominant bond-spin-density-wave correlations for [Formula: see text] in the repulsive regime ([Formula: see text]).
We construct a one-dimensional (1D) theoretical model to clarify the occurrence of superconductivity. The weak-coupling (WC) theory allows a determination of the phase diagram. The constrained hopping induces additional two-body and three-body interactions. At half-filling, the three-body interaction is responsible for the triplet superconducting (TS) correlation. Away from half-filling, the two-body interaction works, favoring the singlet superconducting (SS) correlation. The results are expected to provide an insignificant insight into the superconductivity mechanism.
In the weak-coupling regime, we analytically investigate phase diagram of a one-dimensional half-filled extended Hubbard model with nearest neighboring four-electron interaction (Q), in addition to the usual two-electron couplings (U,V>0). The additional four-electron coupling splits independent Gaussian and spin-gap transitions and also leads to the charge-gap transition. For the positive Q, the ground state exhibits three insulating phases, charge-density-wave (CDW), spin-density-wave (SDW) and bond-spin-density-wave (BSDW). For the negative Q, the phase diagram consists of five phases, which, besides the SDW and CDW phases, contain bond-charge-density-wave (BCDW), Luttinger liquid (LL) and Luther–Emery (LE) phases.