Bose-Fermi N-polaron state emergence from correlation-mediated blocking of phase separation

We investigate the role of interspecies correlations on the localization of impurities immersed in a finite bath of 1D bosonic atoms. Through numerical calculations we show that strong impurity-bath correlations can impede self-localization of the impurities, leading to the emergence of a many-particle polaron state. Specifically, we focus on N fermionic impurities in a one-dimensional lattice bosonic bath at unit filling. Using DMRG and mixed boundary conditions—periodic for bosons, open for fermions— we find a N-polaron ground state replacing phase separation at high interspecies repulsion. This tightly bound state of clustered particles emerges due to the aforementioned strong impurity-bath correlations which induce large impurity-impurity correlations, that we quantify via the von Neumann entropy and bipartite mutual information respectively. This system also reveals a fermionic self-localization effect from a Mott insulator background due to local correlations between the impurities and the bath. The growth of long-range correlations breaks this Mott phase, resulting in the transition to impurity clusters delocalized along the system. We also show that there is a critical impurity number, which depends on intraspecies bosonic interaction, beyond which phase separation is recovered. Finally, we compare these results to calculations in the continuum which show a similar effect.