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.
Analytical continuation of matrix- valued functions: Carath´ eodory formalism.Physical Review B, 104(16):165111, 2021
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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.