TY - JOUR

T1 - On the Kohn-Luttinger conundrum

AU - Hirata, So

AU - He, Xiao

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2013/5/28

Y1 - 2013/5/28

N2 - Kohn and Luttinger [Phys. Rev. 118, 41 (1960)]10.1103/PhysRev.118.41 showed that the conventional finite-temperature extension of the second-order many-body perturbation theory had the incorrect zero-temperature limit in metals and, on this basis, argued that the theory was incorrect. We show that this inconsistency arises from the noninclusion of the temperature effect in the energies of the zeroth-order eigenstates of the perturbation theory, which causes not only the Kohn-Luttinger conundrum but also another inconsistency with the zero-temperature many-body perturbation theory, namely, the different rates of divergence of the correlation energy in a homogeneous electron gas (HEG). We propose a renormalized many-body perturbation theory derivable from the finite-temperature extension of the normal-ordered second quantization applied to the denominators of the energy expression, which involves the energies of the zeroth-order states, as well as to the numerators. The renormalized theory is shown to have the correct zero-temperature limit and the same rate of divergence in a HEG as the zero-temperature counterpart, and is, therefore, the correct finite-temperature many-body perturbation theory.

AB - Kohn and Luttinger [Phys. Rev. 118, 41 (1960)]10.1103/PhysRev.118.41 showed that the conventional finite-temperature extension of the second-order many-body perturbation theory had the incorrect zero-temperature limit in metals and, on this basis, argued that the theory was incorrect. We show that this inconsistency arises from the noninclusion of the temperature effect in the energies of the zeroth-order eigenstates of the perturbation theory, which causes not only the Kohn-Luttinger conundrum but also another inconsistency with the zero-temperature many-body perturbation theory, namely, the different rates of divergence of the correlation energy in a homogeneous electron gas (HEG). We propose a renormalized many-body perturbation theory derivable from the finite-temperature extension of the normal-ordered second quantization applied to the denominators of the energy expression, which involves the energies of the zeroth-order states, as well as to the numerators. The renormalized theory is shown to have the correct zero-temperature limit and the same rate of divergence in a HEG as the zero-temperature counterpart, and is, therefore, the correct finite-temperature many-body perturbation theory.

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U2 - 10.1063/1.4807496

DO - 10.1063/1.4807496

M3 - Article

C2 - 23742459

AN - SCOPUS:84879389465

SN - 0021-9606

VL - 138

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 20

M1 - 204112

ER -