Disordered impenetrable two-component fermions in one dimension

• Published in: arXiv.org
• Main Authors: Kurlov, D V, Bahovadinov, M S, Matveenko, S I, Fedorov, A K, Gritsev, V, Altshuler, B L, Shlyapnikov, G V
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.04.2023
• Subjects: Anderson localization; Boundary conditions; Degrees of freedom; Fermions; Localization; Many body problem; Physics - Disordered Systems and Neural Networks; Physics - Strongly Correlated Electrons
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2112.06895

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion (t-0 model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the t-0 model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.