Bose–Fermi <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-polaron state emergence from correlation-mediated blocking of phase separation

We study <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math> 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 an <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>N</b:mi></b:math>-polaron ground state replacing phase separation at high interspecies repulsion. This tightly bound state of clustered particles emerges due to 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. Finally, we show that there is a critical impurity number, which depends on intraspecies bosonic interaction, beyond which phase separation is recovered.