Diagrammatic Monte Carlo study of a mass-imbalanced Fermi-polaron system

Abstract

We apply the diagrammatic Monte Carlo approach to three-dimensional Fermi-polaron systems with mass-imbalance, where an impurity interacts resonantly with a noninteracting Fermi sea whose atoms have a different mass. This method allows to go beyond frequently used variational techniques by stochastically summing all relevant impurity Feynman diagrams up to a maximum expansion order limited by the sign problem. Polaron energy and quasiparticle residue can be accurately determined over a broad range of impurity masses. Furthermore, the spectral function of an imbalanced polaron demonstrates the stability of the quasiparticle and allows to locate in addition also the repulsive polaron as an excited state. The quantitative exactness of two-particle-hole wave-functions is investigated, resulting in a relative lowering of polaronic energies in the mass-imbalance phase diagram. Tan's contact coefficient for the mass-balanced polaron system is found in good agreement with variational methods. Mass-imbalanced systems can be studied experimentally by ultracold atom mixtures like 6 Li-40 K.

Many Fermi polarons at nonzero temperature

“…Interpretations of polaron experiments in ultracold atomic gases are grounded on the theoretical analyses in which the system with a single impurity at the zero temperature is assumed. In the case of the Fermi polaron whose bath consists of fermions, due to such assumptions, theoretical treatments such as variational methods [25][26][27][28][29][30][31], T-matrix approximation [32][33][34][35], functional renormalization [36,37], and diagrammatic Monte Carlo [38][39][40][41][42] are successfully applied. In the case of finite polarization, the polaron-polaron interaction is discussed [43][44][45][46][47].…”

A stochastic root finding approach: the homotopy analysis method applied to Dyson–Schwinger equations

“…This is again the general procedure leading to the tree expansion. To avoid confusion it should be noted that even though the solution of the nonlinear equation is found in the form of u m f m , å by the HAM this expansion does not constitute the tree expansion as in order to calculate u f j , all u f m , with m j < have to be calculated and stored, see (20). In the sequel we restrict the discussion to a specific nonlinear function n x…”

“…, is the number of monomials b n for the polynomial B m k , . In this notation equation (20) can be written as…”

“…This typically enables the evaluation of the diagrams up to order 5-10 depending on the problem under consideration, from which the converged answer can hopefully be extracted. When taking into account the range of problems, starting with the polaron problem [19][20][21][22] over models of frustrated spins [23,24] and to strongly correlated electron systems [25][26][27][28][29][30], this shows that diagMC is a flexible and quite universal tool. Recently, it has also been used to systematically reintroduce non-local correlations in the dynamical mean-field theory framework [31,32].…”

“…The construction of a rooted tree with height m=6. A fully grown rooted tree corresponds to a single term in the tree expansion which is constructed by recursively applying the definition of the root finding, see equation(20).…”