Finite-temperature second-order many-body perturbation theory revisited

Abstract

We present an algebraic, nondiagrammatic derivation of finite-temperature second-order many-body perturbation theory [FT-MBPT(2)], using techniques and concepts accessible to theoretical chemical physicists. We give explicit expressions not just for the grand potential but particularly for the mean energy of an interacting many-electron system. The framework presented is suitable for computing the energy of a finite or infinite system in contact with a heat and particle bath at finite temperature and chemical potential. FT-MBPT(2) may be applied if the system, at zero temperature, may be described using standard (i.e., zero-temperature) second-order many-body perturbation theory [ZT-MBPT(2)] for the energy. We point out that in such a situation, FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed within ZT-MBPT(2). In other words, the difficulty that has been referred to as the Kohn-Luttinger conundrum, does not occur. We comment, in this context, on a "renormalization" scheme recently proposed by Hirata and He.

Ab Initio Finite Temperature Auxiliary Field Quantum Monte Carlo

“…In recent years, attempts to generalize various ground state post Hartree-Fock methods, such as many-body perturbation 16,17 and coupled-cluster 18 theories, to finite temperature have been made, but this remains an active and growing area of research. [19][20][21] Finite temperature generalizations of density functional theory are becoming increasingly popular in condensed matter physics.…”

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

“…It is then also possible to adjust µ (0) by some root-finding procedure in the framework of the textbook finite-temperature perturbation theory to restore the net charge neutrality [9]. Then, the theory forms a converging series of approximations towards thermal FCI.…”

“…which no longer contains a non-size-consistent term that is a product of two or more extensive quantities. The same expression can be obtained alternatively [9] by returning to equation (31), namely,…”

“…In the previous Chapter [1], we showed that the finite-temperature perturbation theory for electrons described in a number of modern textbooks [2][3][4][5] and excellent reviews [6][7][8][9] does not reproduce the benchmark data obtained as the λ-derivatives of the exact finite-temperature theory [10] with the perturbation-scaled Hamiltonian,Ĥ =Ĥ 0 + λV. The discrepancy was traced [1,11] not so much to mathematical issues but to a misuse of the ensemble.…”

Thermofield theory for finite-temperature quantum chemistry

“…There are a number of reasons for developing finite temperature quantum chemistry, a subject that has recently attracted considerable interest. [7][8][9][10][11][12][13][14][15][16][17][18][19] The finite temperature variants of the coupled cluster method 17,18 are of particular relevance to our present work. These techniques are based on an extension of the time-dependent CC method to imaginary time, and are framed loosely along similar lines as the Thermal Cluster Cumulant theory proposed by Mukherjee et.al., [20][21][22][23] which uses a finite-temperature generalization of Wick's theorem to introduce a thermal normal ordering.…”