Exploring the Fermi polaron problem with canonical-ensemble auxiliary-field quantum Monte Carlo

The behavior of an impurity that interacts strongly with a Fermi sea is of fundamental importance in quantum many-body physics. This system has been realized experimentally in ultra-cold atomic Fermi gases with tunable attractive short-range interactions. In the so-called unitary limit of infinite scattering length, there is a crossover from a dressed quasiparticle, known as the Fermi polaron, at low temperatures to a classical Boltzmann gas at high temperatures. As a function of the interaction strength at zero temperature, there is a transition from a Fermi polaron to a dressed molecule. We explore the thermodynamics of the Fermi polaron problem using canonical-ensemble auxiliary-field quantum Monte Carlo methods by projecting on an N-particle Fermi sea of spin-up particles and on one spin-down particle. Our calculations are carried out on discrete lattices and extrapolated to the continuum limit.