A Non-Gaussian Variational Approach to Fermi Polarons in One- and Two-dimensional Lattices

We study the Fermi polaron problem of one mobile spin-up impurity immersed atop the bath consisting of spin-down fermions in oneand two-dimensional square lattices. We solve this problem by applying a variational approach with non-Gaussian states after separating the impurity and the background via the Lee-Low-Pines transformation. The ground state with a fixed total momentum can be obtained via imaginary-time evolution. For the one-dimensional case, the variational ground-state energy is compared with exact Bethe ansatz solutions and numerical density matrix renormalization-group results with excellent agreement. In two-dimensional lattices, we focus on the dilute limit, and find a polaron-molecule evolution consistent with previous results obtained by variational and quantum Monte Carlo methods for models in continuum space. Compared to previous works, our method provides the lowest ground-state energy in the entire parameter region considered, and has an apparent advantage as it does not need to assume a priori any specific form of the variational wave function.