Results in Physics

Insulating phases driven by unequal on-site repulsion in the 1D unconventional Hubbard model

Yan Xu, Hanqin Ding, Jun Zhang

Published Apr 22, 2021• 2 citations

Abstract

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.

DOI: 10.1016/j.rinp.2021.104206

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Results in Physics

Insulating phases driven by unequal on-site repulsion in the 1D unconventional Hubbard model

Yan Xu, Hanqin Ding, Jun Zhang

Published Apr 22, 2021• 2 citations

Publisher

Abstract

DOI: 10.1016/j.rinp.2021.104206

Related papers

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

Hanqin Ding, Yan Xu, Weiting Chen

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 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.

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arXiv:cond-mat/0308157Physical Review BJan 15, 200478 citations

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Jianhui Dai, Xiaoyong Feng, Tao Xiang +1 more

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We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and

N>2

at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as

-2Nt^2/(N-1)U

in the strong coupling regime. However, the spin gap

Δ_{s}

and the quasiparticle gap

Δ_{1}

as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on

U

such that

Δ_{s}\sim -U(N-1)

and

Δ_{1}\sim -U(N-1)/2

(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,

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.

J

. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as

J

increases, the spin-charge couplings become important and the critical point

{U}_{c}

is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.