Evidence for Many-Body Localization in an Ultracold Fermi-Hubbard Gas

Rahul Nandkishore

William McGehee

We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.

Harmanjeet Kaur, Vinod Ashokan

We investigate the non-equilibrium dynamics of the disordered one-dimensional Fermi-Hubbard model with a focus on many-body localization. The system is initialized in a charge-density-wave-state, and its time evolution is analyzed through sublattice imbalance (spin and charge), and bipartite entanglement entropy. A clear crossover from ergodic to non-ergodic behavior is observed with increasing disorder strength. In the weak disorder regime, rapid decay of imbalance and the fast growth of entanglement indicate efficient thermalization. In contrast, a strong disorder leads to persistent imbalance and slow dynamics, signaling the breakdown of ergodicity. The charge and spin sectors exhibit distinct relaxation behavior, providing evidence for partial decoupling between these degrees of freedom. Furthermore, in the interacting regime, the entanglement entropy shows slow logarithmic growth, reflecting the dephasing-driven dynamics characteristic of the many-body localized phase. These results highlight the interplay between disorder and interactions in determining the dynamical properties of the system and establish robust signatures of many-body localization in the Fermi-Hubbard model.

M. J. Leskinen

Christoph Karrasch, Dante Marvin Kennes, Fabian Heidrich‐Meisner

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.

Pranjal Bordia