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 Mott transition

Even at the filling where band theory predicts a metal, the system can be insulating due to Coulomb interactions between electrons. This type of metal-insulator transition is called the Mott transition, whose properties have been discussed for a long time since the late 1940s. In particlular, since the cuprate high-temperature superconductors are obtained by doping antiferromagnetic Mott insulators with layered structures, electronic properties near the Mott transision in a two-dimensional (2D) system have attracted much attention, and various possibilities have been theoretically proposed, such as the first-order phase transition, divergence of the effective mass in a Fermi liquid, band-insulator-type transition from an antiferromagnetically ordered metal, and slave particle pictures.

 Mott transition of the one-dimensional Hubbard model [1]
As the most simple system with spatial correlations, we consider the Mott transition in a one-dimensional (1D) system. It is known that excitations in a 1D electron system can be primarily explained in terms of spinons, which represent the spin degrees of freedom, and holons, which represent the charge degrees of freedom. As known as the spin-charge separation, the spinon velocity differs with the holon velocity. (This feature contrasts with that predicted by Fermi liquid theory for higher dimensional electronic systems: Fermi liquid theory explains electronic excitations in terms of fermionic quasiparticles having both spin and charge degrees of freedom.) To clarify the nature of the single-particle excitations near the Mott transtion, I calculated the dispersion relations using exact solutions and the single-particle spectral function using the dynamical density matrix renormalization group (DDMRG) method [1]. By comparing the results, I identified the types of excitations for the dominant modes. As a result, the most characteristic feature in the Mott transtion appears in the electron-addition excitations (ω > 0), where strong intensities are located along the upper edge of the spinon-antiholon continuum [1], rather than the region of ω > 0, where the properties of spinon and holon modes have been intensively studied in the context of the spin-charge separation. The mode along the upper edge behaves as a quasiparticle having both spin and charge degrees of freedom. As the doping concentration decreases toward the Mott transiton, the spectral weight of the mode gradually disappears. However, the dispersion relation does not become flat but remains dispersing up to the order of hopping t or spin exchange J (Fig .1). This feature contrasts with the behavior predicted by the Fermi liquid theory with the divergent effective mass m* → ∞. The dispersion relation of the mode in the zero-doping limit has been obtained in the thermodynamic limit by using exact solutions [1]BIn more detail, because the wavenumber of the antiholon is restricted to k = ±2kF in the zero-doping limit, the charge degrees of freedom freezes, whereas the spin degrees of freedom leads continuously to the spinon in the magnetic excitations of the Mott insulator. Thus, although the spectral weight is lost, the dispersion relation remains dispersing in the single-particle spectral function, reflecting the dispersing spin excitations of the Mott insulator. Namely, the Mott transition can be understood as a loss of charge charcter from the mode having both spin and charge degrees of freedom toward the Mott insulator with the spin-charge separation. In other words, from the insulating side, the spin excitation appears in the single-particle excitation spectra by wearing the charge character [1]BIn addition, anomalous electronic features near the Mott transition, such as the hole pocket defined by the region between the two gapless points at k = kF and 2π-3kF and pseudogap bahavior, have been clarified by using exact solutions and highly accurate numerical sumilations [1].

Fig. 1 (a) Single-particle spectral function of the 1D Hubbard model near the Mott transtion [1]. (b) Schematic picture of the dominant modes near the Mott transition. Toward the Mott transiton, the mode for ω > 0 (dotted pink curve) reduces to the spinon dispersion relation indicated by the solid red curve, which is symmetrical with the spinon dispersion relation for ω < 0 with respect to the gapless point at k = kF. Even in the zero-doping limit, it does not become flat [1]. The spectral weight of the mode gradually disappears toward the Mott transition. The region between the two gapless points [intersections of the anti-holon mode (dotted yellow curve for ω > 0) and ω = 0 (solid green line)] can be regarded as a hole pocket, which shrinks as the Mott transition is reached [1]. (c) Dispersion relations of a doped band insulator. (d) Schematic picture of single-particle density of states of a Fermi liquid with divergent effective mass m*. The effective bandwidth shrinks as m* → ∞. Solid green lines indicate ω = 0.

 Mott transition of the two-dimensional Hubbard model [2]
Similar features also appear in the Mott transition of a two-dimensional system [2--6].

In addition, I am interested in critical behaviors [7] and enhancement of superconductiviting correlations [8] near the Mott transition.

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© 2011 Masanori Kohno