Abstract
Understanding the collective behavior of strongly correlated electrons in materials remains a central problem in many-particle quantum physics. A minimal description of these systems is provided by the disordered Fermi-Hubbard model (DFHM), which incorporates the interplay of motion in a disordered lattice with local inter-particle interactions. Despite its minimal elements, many dynamical properties of the DFHM are not well understood, owing to the complexity of systems combining out-of-equilibrium behavior, interactions, and disorder in higher spatial dimensions. Here, we study the relaxation dynamics of doubly occupied lattice sites in the three-dimensional (3D) DFHM using interaction-quench measurements on a quantum simulator composed of fermionic atoms confined in an optical lattice. In addition to observing the widely studied effect of disorder inhibiting relaxation, we find that the cooperation between strong interactions and disorder also leads to the emergence of a dynamical regime characterized by \textit{disorder-enhanced} relaxation. To support these results, we develop an approximate numerical method and a phenomenological model that each capture the essential physics of the decay dynamics. Our results provide a theoretical framework for a previously inaccessible regime of the DFHM and demonstrate the ability of quantum simulators to enable understanding of complex many-body systems through minimal models.
Highlights
Strong disorder and interactions are known to give rise to the celebrated Anderson and Mott metal-insulator transitions
A potential result of combined disorder and interactions in isolated systems is many-body localization (MBL), in which relaxation to thermal equilibrium is prevented by sufficiently strong disorder [7,8,9,10]
In the intermediate disorder regime ( ∼ U ), the observed fast doublon relaxation may be related to the behavior of “bad metals” [36,37], which can be characterized by a lack of conserved excitations [38]
Summary
Strong disorder and interactions are known to give rise to the celebrated Anderson and Mott metal-insulator transitions. Despite a concerted theoretical effort in recent years and several experimental results for one-dimensional chains [11,12,13,14], many questions still remain regarding the nature of this phenomenon This shortcoming is especially true for systems with more than one spatial dimension, initial experimental studies with atoms in two- and three-dimensional optical lattices have observed slow dynamics consistent with MBL [15,16,17]. Reconciling the interplay of slow dynamics caused by doublon binding and disorder-induced localization is critical to obtaining a more complete understanding of thermalization in the DFHM, including the possibility of MBL Advancing this frontier demands exploring the highly nontrivial regime characterized by comparable disorder and interaction energies. We further supplement this picture by developing a simple phenomenological model that incorporates both disorder-enhanced and disorder-suppressed mechanisms for doublon decay
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