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arXiv:cond-mat/9910069 · Journal of the Physical Society of Japan

Effects of Strong Correlation and Randomness in the Vicinity of the Mott Transition in the Quasi-One-Dimensional Hubbard Model

Satoshi Fujimoto

Published Aug 15, 2000• 2 citations
arXivHTMLPDF

Abstract

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 $D_{\perp}\to\infty$ 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 $δ=1-n$ ($n$, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range $l_{\perp}$. We find that the $δ$-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 $δ\to 0$, provided that there exists a finite range interaction.

DOI
10.1143/jpsj.69.2597

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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.
Disordered Hubbard model in d=∞d=\inftyd=∞
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We discuss the transition from a metal to charge- or spin-insulating phases characterized by the opening of a gap in the charge- or spin-excitation spectra, respectively. These transitions are addressed within the context of two exactly solvable Hubbard and t-J chains with long-range, 1/r hopping. We discuss the specific heat, compressibility, and magnetic susceptibility of these models as a function of temperature, the band filling, and the interaction strength. We then use conformal-field-theory techniques to extract ground-state correlation functions. Finally, by employing the g-ology analysis we show that the charge-insulator transition is accompanied by an infinite discontinuity in the Drude weight of the electrical conductivity. While the magnetic properties of these models reflect the genuine features of strongly correlated electron systems, the charge-transport properties, especially near the Mott-Hubbard transition, display a nongeneric behavior.
A brief introduction to the bosonization method for interacting one-dimensional fermion systems is given. Using these results, the long-distance decay of correlation functions in the one-dimensional Hubbard model is determined exactly for arbitrary bandfilling and correlation strength, using the exact solution of Lieb and Wu. For infinite U the results are generalized to the case of nonzero nearest-neighbour interaction. The behaviour of thermodynamic quantities, of the frequency-dependent conductivity, and of the thermopower is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half- and quarter-filling. The one-dimensional Luttinger liquid is shown to be unstable in the presence of interchain hopping. The results for the metal-insulator transition are compared with other scenarios developed in higher dimensions.
A brief introduction to the bosonization method for interacting one-dimensional fermion systems is given. Using these results, the long-distance decay of correlation functions in the one-dimensional Hubbard model is determined exactly for arbitrary bandfilling and correlation strength, using the exact solution of Lieb and Wu. For infinite U the results are generalized to the case of nonzero nearest-neighbour interaction. The behaviour of thermodynamic quantities, of the frequency-dependent conductivity, and of the thermopower is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half- and quarter-filling. The one-dimensional Luttinger liquid is shown to be unstable in the presence of interchain hopping. The results for the metal-insulator transition are compared with other scenarios developed in higher dimensions.