The paper proves existence and, in a smaller parameter range, uniqueness of solutions to a Matsubara frequency discretization of the IPT-DMFT equations, analyzes the Hubbard dimer, and reports numerical evidence that discretized solutions can fail the Pick interpolation criterion.
Interpolation by pick functions.Monotone Matrix Functions and Analytic Continuation, pages 117–127, 1974
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A mathematical analysis of the discretized IPT-DMFT equations
The paper proves existence and, in a smaller parameter range, uniqueness of solutions to a Matsubara frequency discretization of the IPT-DMFT equations, analyzes the Hubbard dimer, and reports numerical evidence that discretized solutions can fail the Pick interpolation criterion.