Related papers: The Spectrum of the Almost Mathieu Operator
We report on the dramatic slowing down of the charge carrier dynamics in a quasi-two-dimensional organic conductor, which can be reversibly tuned through the Mott metal-insulator transition (MIT). At the finite-temperature critical endpoint…
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and…
We study the properties of a quarter-filled system of electrons on a square lattice interacting through a local repulsion $U$ and a nearest-neighbour repulsion $V$ in the limit $V=+\infty$. We identify the ground-state for $U$ large enough…
The double-exchange model for the Mn oxides with orbital degeneracy is studied with including on-site Coulomb repulsion, Jahn-Teller (J-T) coupling and doping-induced disorder. In the strong interaction limit, it is mapped onto a…
This paper focuses on the fractal characteristics of the absolutely continuous spectral measure of the subcritical almost Mathieu operator (AMO) and Diophantine frequency. In particular, we give a complete description of the (classical)…
Unusual metallic states involving breakdown of the standard Fermi-liquid picture of long-lived quasiparticles in well-defined band states emerge at low temperatures near correlation-driven Mott transitions. Prominent examples are…
A brief review of metal-insulator transitions in three-dimensional doped semiconductors, with emphasis on the "critical exponent puzzle"; and new experimental findings that signal the possibility of an unexpected metal-insulator transition…
This is the write-up of the talk I gave at the 23rd International Symposium on Mathematical Programming (ISMP) in Bordeaux, France, July 6th, 2018. The talk was a general overview of the state of the art of time-varying, mainly convex,…
We study the electronic structure and correlations in the geometrically frustrated two dimensional checkerboard lattice. In the large U limit considered here we start from an extended Hubbard model of spinless fermions at half-filling. We…
We study the metal-to-insulator transition of the Hubbard model at zero temperatures in infinite dimensions. The coexistence of metallic and insulating solutions for a finite range of the interaction is established. It is shown that the…
For the S-states of muonium and positronium, the hyperfine shifts to the order $\alpha^6$ of a recently derived two-fermion equation with explicit $\cal CPT$-invariance are checked against the results of a nonrelativistic reduction, and the…
Multilayer (TiO$_2$)$_m$/(VO$_2$)$_n$ nanostructures ($d^1$ - $d^0$ interfaces with no polar discontinuity) show a metal-insulator transition with respect to the VO$_2$ layer thickness in first principles calculations. For $n$ $\geq$ 5…
A possibility of a metal-insulator transition in molecular conductors has been studied for systems composed of donor molecules and fully ionized anions with an incommensurate ratio close to 2:1 based on a one-dimensional extended Hubbard…
We review recent experimental results on the metal-insulator transition and low-density phases in strongly-interacting, low-disordered Si-based two-dimensional electron systems. Special attention is given to the metallic state in…
This largely pedagogical paper recalls some facts on defect numbers of products of closed operators employing results from the theory of semi-Fredholm operators and then applies these facts to positive integer powers of symmetric operators…
A brief report of the topics which received attention during the discussion session II of the International Workshop on Symmetries and Low-Energy Phase Transitions in Nuclear-Structure Physics, held in Camerino on 9-11 October 2005, is…
We found direct experimental evidence for an orbital switching in the V 3d states across the metal-insulator transition in VO$_{2}$. We have used soft-x-ray absorption spectroscopy at the V $L_{2,3}$ edges as a sensitive local probe, and…
An instability of the quasi-1D Luttinger liquid associated with the metal - insulator transition is considered. The homogeneous metal ground state of this liquid is demonstrated to be unstable and the charge-density wave arises in the…
We study the quantum phase transition from an insulator to a metal realized at t'=t'_c > 0.5t in the ground state of the half-filled Hubbard chain with both nearest-neighbor (t) and next-nearest-neighbor (t') hopping. The study is carried…
We consider separable 2D discrete Schr\"odinger operators generated by 1D almost Mathieu operators. For fixed Diophantine frequencies we prove that for sufficiently small couplings the spectrum must be an interval. This complements a result…