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arXiv:cond-mat/9407015 · Physical review. B, Condensed matter

Influence of long-range Coulomb interaction on the metal-insulator transition in one-dimensional strongly correlated electron systems

Ilya V. Krive, A. A. Nersesyan, M. Jonson, Robert I Shekhter

Published Oct 15, 1995• 6 citations
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Abstract

We study the influence of long-range Coulomb interactions on the properties of one-dimensional (1D) strongly correlated electron systems in the vicinity of the metal-insulator Mott-Hubbard phase transition. It is shown that, in the metallic phase, the standard square-root singularity of the compressibility at the transition point changes to a logarithmic one, due to the formation of a 1D Wigner crystal of solitons (holons). On increasing the soliton density in a finite-size chain, the behavior of the compressibilty reflects a sequence of crossovers between classical, low-density regimes of perfectly or nearly ordered Wigner-crystal states, and quantum regimes of a nearly free Fermi gas of solitons, followed (in the high-density limit) by a liquid phase of strongly correlated solitons. In a mesoscopic situation, where the screening length in a 1D chain is controlled by a massive electrode (gate) placed near the chain, there is a narrow region near the transition point where quantum fluctuations melt the Wigner crystal and recover the universal square-root singularity of the compressibility. Strong Coulomb interaction affects the formation of the charge excitations in the insulating phase, transforming the sine-Gordon solitons into quasiclassical Coulomb solitons. Multiplicative logarithmic renormalizations of the characteristic soliton size and rest energy are found.

DOI
10.1103/physrevb.52.10865

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We study the influence of long-range Coulomb interactions on the properties of one-dimensional (1D) strongly correlated electron systems in the vicinity of the metal-insulator Mott-Hubbard phase transition. It is shown that, in the metallic phase, the standard square-root singularity of the compressibility at the transition point changes to a logarithmic one, due to the formation of a 1D Wigner crystal of solitons (holons). On increasing the soliton density in a finite-size chain, the behavior of the compressibilty reflects a sequence of crossovers between classical, low-density regimes of perfectly or nearly ordered Wigner-crystal states, and quantum regimes of a nearly free Fermi gas of solitons, followed (in the high-density limit) by a liquid phase of strongly correlated solitons. In a mesoscopic situation, where the screening length in a 1D chain is controlled by a massive electrode (gate) placed near the chain, there is a narrow region near the transition point where quantum fluctuations melt the Wigner crystal and recover the universal square-root singularity of the compressibility. Strong Coulomb interaction affects the formation of the charge excitations in the insulating phase, transforming the sine-Gordon solitons into quasiclassical Coulomb solitons. Multiplicative logarithmic renormalizations of the characteristic soliton size and rest energy are found.
Experiments on quasi-one-dimensional systems such as quantum wires and metallic chains on surfaces suggest the existence of electron-electron interactions of substantial range and hence physics beyond the Hubbard model. We therefore investigate one-dimensional, quarter-filled chains with a Coulomb potential with variable screening length by quantum Monte Carlo methods and exact diagonalization. The Luttinger liquid interaction parameter ${K}_{\ensuremath{\rho}}$ decreases with increasing interaction strength and range. Experimentally observed values close to 1/4 require strong interactions and/or large screening lengths. As predicted by bosonization, we find a metal-insulator transition at ${K}_{\ensuremath{\rho}}=1/4$. Upon increasing the screening length, the charge and spin correlation functions reveal the crossover from dominant 2kF2{k}_{\mathrm{F}}2kF​ spin correlations to dominant 4kF4{k}_{\mathrm{F}}4kF​ charge correlations, and a strong enhancement of the charge velocity. In the metallic phase, the signatures of spin-charge separation in the single-particle spectrum, spinon and holon bands, remain robust even for rather long-ranged interactions. The charge-density-wave state exhibits backfolded shadow bands.
We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number D⊥→∞D_{\perp}\to\inftyD⊥​→∞ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping δ=1−nδ=1-nδ=1−n (nnn, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range l⊥l_{\perp}l⊥​. We find that the δδδ-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for δ→0δ\to 0δ→0, provided that there exists a finite range interaction.
The effects of a long-range electronic potential on a one-dimensional chain of spinless fermions are investigated by numerical techniques (exact diagonalization of rings with up to 30 sites complemented by finite size analysis) and analytic calculations. Due to a competition between the 2kF{2k}_{F}2kF​ oscillations in the density and the (very slow) log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) length scales. Despite some similarities, we found that this quasimetallic regime is not of the Luttinger liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substantially increased, we observe a smooth crossover to a strongly localized charge density wave.
Continuous Wigner-Mott transition at ν=1/5ν=1/5ν=1/5
Electrons can organize themselves into charge-ordered states to minimize the effects of long-ranged Coulomb interactions. In the presence of a lattice, commensurability constraints lead to the emergence of incompressible Wigner-Mott insulators at various rational electron fillings, ν =p/qν~=p/qν =p/q. The mechanism for quantum fluctuation-mediated melting of the Mott insulators with increasing electron kinetic energy remains an outstanding problem. Here, using matrix product state techniques, we analyze the bandwidth-tuned transition out of the Wigner-Mott insulator at ν=1/5ν=1/5ν=1/5 in an extended Hubbard model on infinite cylinders of varying circumference. For the two-leg ladder, the transition from the Mott insulator to the Luttinger liquid proceeds via a distinct intermediate phase with gapless Cooper-pairs and gapped electronic excitations. The resulting Luther-Emery liquid is the analog of a strongly fluctuating superconductor. We place these results in the context of a low-energy bosonization based theory for the transition. On the five-leg cylinder, we provide numerical evidence for a direct continuous transition between the Wigner-Mott insulator and a metallic phase across which the spin and charge-gaps vanish simultaneously. We comment on the connections to ongoing experiments in dual-gated bilayer moiré transition metal dichalcogenide materials.
The relationship among the Wigner crystal, charge ordering, and the Mott insulator is studied by the path-integral renormalization group method in two-dimensional systems with long-range Coulomb interaction. In contrast to the insensitivity of the Hartree-Fock results, the stability of the solid drastically decreases with the decrease in the lattice commensurability. The transition to liquid occurs at the electron gas parameter r(s) approximately 2 for the filling n=1/2, showing a large reduction from r(s) approximately 35 in the continuum limit. A correct account of quantum fluctuations is crucial to understanding the charge-order stability generally observed only at simple fractional fillings and the nature of quantum liquids away from them.
We explore the role of electron correlation in quasi-one-dimensional quantum wires as the range of the interaction potential is changed and their thickness is varied by performing exact quantum Monte Carlo simulations at various electronic densities. In the case of unscreened interactions with a long-range 1/x1/x1/x tail there is a crossover from a liquid to a quasi-Wigner crystal state as the density decreases. When this interaction is screened, quasi-long-range order is prevented from forming, although a significant correlation with 4kF4{k}_{F}4kF​ periodicity is still present at low densities. At even lower electron concentration, exchange is suppressed and the electrons behave like spinless fermions. Finally, we study the effect of electron correlations in the double quantum wire experiment [Steinberg et al., Phys. Rev. B 73, 113307 (2006)] by introducing an accurate model for the screening in the experiment and explicitly including the finite length of the system in our simulations. We find that decreasing the electron density continuously drives the system from a liquid to a state with quite strong 4kF4{k}_{F}4kF​ correlations. This crossover takes place around $22\text{ }\ensuremath{\mu}{\text{m}}^{\ensuremath{-}1}$, near the density where the electron localization occurs in the experiment. The charge and spin velocities are also in good agreement with the experimental findings in the proximity of the crossover. We argue that correlation effects play an important role at the onset of the localization transition.