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Properties of Interacting Fermions in Disordered Systems.

Lawrence Ira Fleishman

Published Jan 1, 1978• 0 citations
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Many-body localization of fermions with tunable interactions in a lattice with Moiré-type quasiperiodic disorder

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Abstract There are exceptions to the general observation that interacting quantum-many body systems thermalize. The most prominent case is many-body localization (MBL) where interactions drive localization in disordered lattice systems. In such systems, the eigenstate thermalization (ETH) hypothesis breaks down and the system remains in a non-thermal state. The existence of MBL in two-dimensional systems and the conditions on required disorder properties are still debated. Here, we study a two-dimensional fermionic quantum many-body system in Moiré-type quasiperiodic disorder and find a novel two-step transition to a MBL state. The intermediate state shows anisotropic transport induced by partial localization. Our work paves the way for the study of the numerous intriguing phenomena observed in Moiré lattice materials and our observations ask for further studies on localization in more complex Moiré structures.

•Nov 13, 2025•0 citations
A fermionic disordered one-dimensional wire in the presence of attractive interactions is known to have two distinct phases, a localized and superconducting, depending on the strength of interaction and disorder. The localized region may also exhibit a metallic behavior if the system size is shorter than the localization length. Here we show that the superconducting phase has a distribution of the entanglement entropy distinct from the metallic regime. The entanglement entropy distribution is strongly asymmetric with a Lévy α-stable distribution (compared to the Gaussian metallic distribution), as is seen also for the second Rényi entropy distribution. Thus, entanglement properties may reveal properties which cannot be detected by other methods.
Abstract There are exceptions to the general observation that interacting quantum-many body systems thermalize. The most prominent case is many-body localization (MBL) where interactions drive localization in disordered lattice systems. In such systems, the eigenstate thermalization (ETH) hypothesis breaks down and the system remains in a non-thermal state. The existence of MBL in two-dimensional systems and the conditions on required disorder properties are still debated. Here, we study a two-dimensional fermionic quantum many-body system in Moiré-type quasiperiodic disorder and find a novel two-step transition to a MBL state. The intermediate state shows anisotropic transport induced by partial localization. Our work paves the way for the study of the numerous intriguing phenomena observed in Moiré lattice materials and our observations ask for further studies on localization in more complex Moiré structures.