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Results in Physics

Ground-state instabilities in a Hubbard-type chain with particular correlated hopping at non-half-filling

Weiting Chen, Jun Zhang, Hanqin Ding

Published Apr 24, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2023.106472

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Modern Physics Letters B•Feb 20, 2012•5 citations
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.
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.
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.
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.
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.