Signatures of many-body localization in a two-dimensional lattice of ultracold polar molecules with disordered filling

In this talk, we present our work exploring many-body localization (MBL) in systems of ultracold polar molecules in two-dimensional optical lattices. Specifically, we investigate a novel form of ergodicity breaking that arises in systems of ultracold polar molecules due to non-unit lattice fillings. We study the scenario where two well isolated rotational states form an effective spin-1/2 degree of freedom, allowing the molecules to realise a dipolar spin-1/2 Hamiltonian with microscopic parameters tunable via precise control of an external DC electric field. We perform large-scale exact diagonalization simulations to explore the non-equilibrium dynamics and eigenstate properties for systems of up to 16 molecules at 50% lattice filling. We observe several key signatures of MBL as the relative strength of the spin-density interactions is increased, including retention of initial state memory in the system’s long-time dynamics and logarithmic growth of bipartite entanglement entropy. Additionally, we find evidence for divergent entanglement entropy fluctuations close to the critical disorder strength W_c. We extract an estimate for W_c and the critical exponents of the MBL transition in the thermodynamic limit via finite-size scaling analysis. We demonstrate that the results of our dynamical simulations are consistent with an observed crossover behviour in the level-spacing statistics of the many-body Hamiltonian, which is a well known indicator of the thermal to MBL phase transition. Our results are realisable in current molecular quantum gas microscope experiments, and we discuss possible experimental considerations. Our proposal paves the way for studies of many-body localization in higher-dimensional dipolar spin models and highlights the potential for quantum simulation of non-equilibrium dynamics in current state of-the-art ultracold polar molecule platforms.