Exact theory of the finite-temperature spectral function of Fermi polarons with multiple particle-hole excitations: Diagrammatic theory versus Chevy ansatz
arxiv(2024)
摘要
By using both diagrammatic theory and Chevy ansatz approach, we derive an
exact set of equations, which determines the spectral function of Fermi
polarons with multiple particle-hole excitations at nonzero temperature. In the
diagrammatic theory, we find out the complete series of Feynman diagrams for
the multi-particle vertex functions, when the unregularized contact interaction
strength becomes infinitesimal, a typical situation occurring in two- or three-
dimensional free space. The latter Chevy ansatz approach is more widely
applicable, allowing a nonzero interaction strength. We clarify the equivalence
of the two approaches for an infinitesimal interaction strength and show that
the variational coefficients in the Chevy ansatz are precisely the on-shell
multi-particle vertex functions divided by an excitation energy. Truncated to a
particular order of particle-hole excitations, our exact set of equations can
be used to numerically calculate the finite-temperature polaron spectral
function, once the numerical singularities in the equations are appropriately
treated. As a concrete example, we calculate the finite-temperature spectral
function of Fermi polarons in one-dimensional lattices, taking into account all
the two-particle-hole excitations. We show that the inclusion of
two-particle-hole excitations quantitatively improve the predictions on the
polaron spectral function. Our results provide a useful way to solve the
challenge problem of accurately predicting the finite-temperature spectral
function of Fermi polarons in three-dimensional free space. In addition, our
clarification of the complete set of Feynman diagrams for the multi-particle
polaron vertex functions may inspire the development of more accurate
diagrammatic theories of population-imbalanced strongly interacting Fermi
gases, beyond the conventional many-body T-matrix approximation.
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