# The Kohn-Luttinger conundrum redux: Failure of finite-temperature many-body perturbation theory at low temperatures

@inproceedings{Hirata2020TheKC, title={The Kohn-Luttinger conundrum redux: Failure of finite-temperature many-body perturbation theory at low temperatures}, author={So Hirata}, year={2020} }

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy of the ground state as a function of the perturbation strength either touches or crosses the energy function of an excited state. Contrary to earlier assertions concerning the role played by the chemical potential, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the…

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## References

SHOWING 1-10 OF 17 REFERENCES

On the Kohn-Luttinger conundrum.

- PhysicsThe Journal of chemical physics
- 2013

The 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, is shown to have the correct zero-Temperature limit and the same rate of divergence in a HEG as the zero-tem temperature counterpart.

Numerical evidence invalidating finite-temperature many-body perturbation theory

- PhysicsAnnual Reports in Computational Chemistry
- 2019

Converging finite-temperature many-body perturbation theory in the grand canonical ensemble that conserves the average number of electrons

- PhysicsAnnual Reports in Computational Chemistry
- 2019

Finite-temperature many-body perturbation theory in the grand canonical ensemble.

- PhysicsThe Journal of chemical physics
- 2020

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing.…

Finite-temperature many-body perturbation theory in the canonical ensemble.

- Physics, ChemistryPhysical review. E
- 2020

Sum-over-states analytical formulas for up to the third-order corrections to these properties are derived as analytical λ-derivatives and should be valid for both degenerate and nondegenerate reference states at any temperature down to zero.

Finite-temperature full configuration interaction

- Physics, ChemistryTheoretical Chemistry Accounts
- 2014

The exact basis-set values of various thermodynamic potentials of a molecule are evaluated by the finite-temperature full configuration-interaction (FCI) method using ab initio molecular integrals…

One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms.

- MathematicsThe Journal of chemical physics
- 2017

The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework.

Note on an Approximation Treatment for Many-Electron Systems

- Physics
- 1934

A perturbation theory is developed for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation. It is shown by this development that the first…