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We consider a fermionic many body system in Zd with a short range interaction and quasi-periodic disorder. In the strong disorder regime and assuming a Diophantine condition on the frequencies and on the chemical potential, we prove at $T=0$ the exponential decay of the correlations and the vanishing of the Drude weight, signaling Anderson localization in the ground state. The proof combines Ward Identities, Renormalization Group and KAM Lindstedt series methods.
Interacting spinning fermions with strong quasi-random disorder are analyzed via rigorous Renormalization Group (RG) methods combined with KAM techniques. The correlations are written in terms of an expansion whose convergence follows from number-the
In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the top and bott
A microwave setup for mode-resolved transport measurement in quasi-one-dimensional (quasi-1D) structures is presented. We will demonstrate a technique for direct measurement of the Greens function of the system. With its help we will investigate quas
We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case localization persist
We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional has a minimi