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Results in Physics

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

Xin Sun, Liyue Wang, Hanqin Ding

Published Aug 23, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2024.107925

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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-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.
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.
We determine the ground-state phase diagram for the 1/r1/r1/r-Hubbard model with repulsive nearest-neighbor interaction at half band filling using the density-matrix renormalization group method. Due to the absence of Umklapp scattering, the phase diagram displays finite regions for the three generic phases, namely, a Luttinger liquid metal for weak interactions, a Mott-Hubbard insulator for dominant Hubbard interactions, and a charge-density-wave insulator for dominant nearest-neighbor interactions. Up to moderate interaction strengths, the quantum phase transitions between the metallic and insulating phases are continuous, i.e., the gap opens continuously as a function of the interaction strength. We conclude that generic short-range interactions do not change the nature of the Mott transition qualitatively.