Abstract
We consider a fermionic many body system in {mathbb Z}^d 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 non-metallic behavior in the ground state. The proof combines Ward Identities, Renormalization Group and KAM Lindstedt series methods.
Highlights
The conductivity properties in fermionic systems, describing electrons in metals, are strongly affected by the presence of disorder, which breaks the perfect periodicity of an ideal lattice and is unavoidable in real systems
In absence of many body interaction disorder produces the phenomenon of Anderson localization [1], consisting in an exponential decay of all eigenstates and in an insulating behavior with vanishing conductivity
With random disorder Anderson localization was established for strong disorder in any dimension [2,3] and in one dimension with any disorder
Summary
The conductivity properties in fermionic systems, describing electrons in metals, are strongly affected by the presence of disorder, which breaks the perfect periodicity of an ideal lattice and is unavoidable in real systems. In absence of many body interaction disorder produces the phenomenon of Anderson localization [1], consisting in an exponential decay of all eigenstates and in an insulating behavior with vanishing conductivity. Such a phenomenon relies on the properties of the single particle Schroedinger equation and it has been the subject of a deep mathematical investigation. With random disorder Anderson localization was established for strong disorder in any dimension [2,3] and in one dimension with any disorder.
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