Impurities in One Dimension

Daniel F. Calef

D. Huber, H.‐W. Hammer, Artem G. Volosniev

The medium around impurity particles modifies their bare interaction such that even impurities with repulsive bare interactions can form bound states in the medium. The paper studies this counterintuitive phenomenon using exactly solvable and effective models in one dimension.

Lilith Zschetzsche, Robert E. Zillich

We investigate self-localization of a polaron in a homogeneous Bose-Einstein condensate in one dimension. This effect, where an impurity is trapped by the deformation that it causes in the surrounding Bose gas, has been first predicted by mean-field calculations, but has not been seen in experiments. We study the system in one dimension, where, according to the mean-field approximation, the self-localization effect is particularly robust and present for arbitrarily weak impurity-boson interactions. We address the question whether self-localization is a real effect by developing a variational method which incorporates impurity-boson correlations nonperturbatively and solving the resulting inhomogeneous correlated polaron equations. We find that correlations inhibit self-localization except for very strongly repulsive or attractive impurity-boson interactions. Our prediction for the critical interaction strength for self-localization agrees with a sharp drop of the inverse effective mass found in quantum Monte Carlo simulations of polarons in one dimension. Published by the American Physical Society 2024

Victor J. Emery, Steven Allan Kivelson

Igor N. Karnaukhov

Artem G. Volosniev, H.‐W. Hammer

We discuss the ground-state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparison to exact quantum Monte Carlo calculations. In addition, we test the method in finite-size systems using numerical results based upon the similarity renormalization group. We argue that the introduced approach provides a simple analytical tool for studies of strongly interacting impurity problems in one dimension.