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Scientific Reports

Unequal on-site interaction effects in the one-dimensional electron system at quarter filling

Hanqin Ding, Yan Xu, Weiting Chen

Published May 24, 2021• 3 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-021-90336-x

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arXiv:cond-mat/0308157•Physical Review B•Jan 15, 2004•78 citations
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 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.
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 bosonization approach and the weak-coupling renormalization group (RG) techniques, we study the phase diagram of one-dimensional half-filled t–U–J model parametrized by exchange anisotropy λ (0 ≤ λ ≤ 2) in the weak-coupling regime. In the case of anisotropic antiferromagnetic exchange (J > 0) and on-site repulsion (U > 0), the ground state is characterized by the spin-density-wave (SDW) and bond-charge-density-wave (BCDW) insulating phases. We identify the SDW correlation corresponding to the transverse SDW± phases with a gapless spin excitation (Δs=0) for λ < 4/3 and to the longitudinal SDWz phase with a spin gap (Δs > 0) for λ > 4/3, respectively. The charge excitation is always gapped (Δc > 0) in the whole regime, and the BCDW and SDWz phases show a long-range order. We also examine effects of the nonlocal Umklapp scattering of parallel-spin electrons, which play a role to weaken the BCDW phase and to enhance the SDW phase slightly. The results demonstrate that the properties of our model are not identical with those of the conventional t–U–J 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.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.