Mott Transition in the Hubbard Model
نویسنده
چکیده
In this article, I discuss W.Kohn’s criterion for a metal insulator transition, within the framework of a one band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some intersting miscellaneous results discussed. The Jordan Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the “extra phases” arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e. diamagnetism), and the corresponding “happy fluxes” for the fermions identified. A curious result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A “spin-statistics” like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out.
منابع مشابه
Breakdown of the Luttinger sum - rule at the Mott - Hubbard transition in the one - dimensional t 1 − t 2 Hubbard model .
– We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1 − t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting...
متن کاملMott transition in the two-dimensional Hubbard model.
Spectral properties of the two-dimensional Hubbard model near the Mott transition are investigated by using cluster perturbation theory. The Mott transition is characterized by freezing of the charge degrees of freedom in a single-particle excitation that leads continuously to the magnetic excitation of the Mott insulator. Various anomalous spectral features observed in cuprate high-temperature...
متن کاملQuantum phase transition from a Mott insulator to a superfluid in bosons
Bose Hubbard model is presented and basic natures of Mott insulating phase and superfluid phase are studied in this essay. Also how and when this quantum phase transition occurs is discussed. Experimental supports from ultracold atoms physics are explained, while some miscellaneous topics are touched in the end.
متن کاملNature of the Peierls - to Mott - insulator transition in 1 D
In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional halffilled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on ...
متن کاملMetal-insulator transitions in the periodic Anderson model.
We solve the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean field theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely, with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator ...
متن کامل3 0 Ju l 2 00 4 Two Aspects of the Mott - Hubbard Transition in Cr - doped V 2 O 3
The combination of bandstructure theory in the local density approximation with dynamical mean field theory was recently successfully applied to V2O3 – a material which undergoes the famous Mott-Hubbard metal-insulator transition upon Cr doping. The aim of this short paper is to emphasize two aspects of our recent results: (i) the filling of the Mott-Hubbard gap with increasing temperature, and...
متن کامل