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Indian Journal of Physics

Many-body localization properties of disordered interacting fermionic systems

Kanabet Yapara, E. N. Djoukouo, Celsus Bouri, M. H. B. Mackongo, M.G. Kwato Njock

Published Sep 8, 2024• 0 citations
Publisher
DOI
10.1007/s12648-024-03399-7

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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.
Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. In a class of one-dimensional spinless fermionic models with random disorder, we study the finite-size scaling of the ratio of typical to average values of the single-particle local density of states and the scattering rates across the MBL transition. Our results indicate that the MBL transition in this class of one-dimensional models of spinless fermions is continuous in nature. For various ranges of interactions in the system, the critical exponent $\ensuremath{\nu}$ with which the correlation length $\ensuremath{\xi}$ diverges at the transition point ${W}_{c}, \ensuremath{\xi}\ensuremath{\sim}|W\ensuremath{-}{W}_{c}{|}^{\ensuremath{-}\ensuremath{\nu}}$, satisfies the Chayes-Chayes-Fisher-Spencer (CCFS) bound $\ensuremath{\nu}\ensuremath{\ge}2/d$ where ddd is the physical dimension of the system. We also discuss why the critical exponent obtained from finite-size scaling of the conventional diagnostic of many-body localization, the level spacing ratio, strongly violates the CCFS bound while the single-particle density of states and scattering rates are consistent with the CCFS criterion.
Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions.