Localization in an interacting quasi-periodic fermionic chain

Abstract

We consider a many body fermionic system with an incommensurate external potential and a short range interaction in one dimension. We prove that, for certain densities and weak interactions, the zero temperature thermodynamical correlations are exponentially decaying for large distances, a property indicating persistence of localization in the interacting ground state. The analysis is based on Renormalization Group, and convergence of the renormalized expansion is achieved using fermionic cancellations and controlling the small divisor problem assuming a Diophantine condition for the frequency.

24 pages, 5 figures

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• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Integrals of motion in the Many-Body localized phase
• Many-Body Localization in a Quasiperiodic System
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Cited by in corpus (9)

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• Manifestations of dynamical localization in the disordered XXZ spin chain
• Stability of Weyl semimetals with quasiperiodic disorder
• Dense gaps and scaling relations in the interacting Aubry-Andre' model
• Coupled identical localized fermionic chains with quasi-random disorder
• Interacting spinning fermions with quasi-random disorder
• Localization in the random XXZ quantum spin chain
• Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder