Absence of self-localization of quantum impuritys in 1D Bose gases

Utilizing Tensor Network simulation we numerically probe the ground state of mobile quantum impurities in 1D Bose gases trapped in a box potential.

We observe a transition between a delocalized impurity and an impurity localized at the system boundaries, as a function of Impurity-Bose interaction strength. While this transition can reasonably be predicted by a mean-field ansatz based on coupled Gross-Pitaevski - Schrödinger equations, the mean-field ansatz also suggests the existence of a self-localized polaron solution. We show that the self-localization is an artifact of the underlying decoupling approximation. This shows that even for weak bose-bose interactions, where mean-field approaches are expected to work well, Impurity-Bose correlations are important for representing the true behavior of the system.

We also give analytical predictions for the critical Bose-Impurity interaction strength, for which these phase transitions occur.