Lowtemperature breakdown of manybody perturbation theory for thermodynamics
Abstract
It is shown analytically and numerically that the finitetemperature manybody perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the firstorder HirschfelderCertain degenerate perturbation theory, the secondorder grand potential and internal energy diverge as T →0 . Contrary to earlier suggestions of renormalizability by the chemical potential μ , this nonconvergence, first suspected by Kohn and Luttinger, is caused by the nonanalytic nature of the Boltzmann factor e^{E /kBT} at T =0 , also plaguing the canonical ensemble, which does not involve μ . The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of powerseries expansions and is unlikely to be removed within its framework.
 Publication:

Physical Review A
 Pub Date:
 January 2021
 DOI:
 10.1103/PhysRevA.103.012223
 arXiv:
 arXiv:2006.00078
 Bibcode:
 2021PhRvA.103a2223H
 Keywords:

 Physics  Chemical Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 Phys. Rev. A 103, 012223 (2021)