Numerical evidence invalidating finite-temperature many-body perturbation theory

Abstract

Low-order perturbation corrections to the electronic grand potential, internal energy, chemical potential, and entropy of an ideal gas of noninteracting, identical molecules at a nonzero temperature are determined numerically as the λ-derivatives of the respective quantity calculated exactly (by thermal full configuration interaction) with a perturbation-scaled Hamiltonian,Ĥ 0 + λV. The data thus obtained from the core definition of any perturbation theory serve as a benchmark against which analytical formulas can be validated. The first-and second-order corrections from finite-temperature many-body perturbation theory discussed in many textbooks disagree with these benchmark data. This is because the theory neglects the variation of chemical potential with λ, thereby failing to converge at the exact, full-interaction (λ = 1) limit, unless the exact chemical potential is known in advance. The renormalized finite-temperature perturbation theory [S. Hirata and X. He, J. Chem. Phys., 138, 204112 (2013)] is also found to be incorrect.

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium

“…Recently, there has been a resurgence of interest in this topic. Many attempts have been made to obtain a time-dependent coupled cluster (TDCC) or many-body perturbation theory (MBPT) formulation for directly calculating thermal properties of quantum many-body systems. − However, most of these works focus on either pure electronic systems or single-surface pure vibrational systems. In this work, we develop an approach for multi-surface vibronic coupling systems.…”

On the Chemical Potential of Many-Body Perturbation Theory in Extended Systems

“…At higher temperatures, a large number of one-body states is occupied with non-negligible probabilities. Orbital-free density functional theories (ofDFT) aim at mitigating this with functionals that do not depend on the usual Kohn–Sham orbital description of DFT. , Canonical or grand-canonical full configuration interaction methods can be used for benchmarking more approximate theories . Finally, various forms of Monte Carlo methods approach the finite-temperature many-body problem in complementary ways as they exhibit entirely different error sources.…”

“…41,42 Canonical or grand-canonical full configuration interaction methods can be used for benchmarking more approximate theories. 43 Finally, various forms of Monte Carlo methods approach the finitetemperature many-body problem in complementary ways as they exhibit entirely different error sources. They include pathintegral Quantum Monte Carlo (PIQMC) calculations, 3,4 Density Matrix Quamtum Monte Carlo (DMQMC) calculations, 44−46 and Auxiliary Field Quantum Monte Carlo (AFQMC) calculations.…”

Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble

“…The past few years, for example, have seen a resurgence of interest in finite temperature coupled cluster techniques [18][19][20][21][22] and perturbation theories. [23][24][25][26][27][28] Closer to the mean field end of the spectrum, finite temperature embedding theories that partition systems into correlated regions embedded within uncorrelated baths 29 such as Dynamical Mean Field Theory (DMFT) 30,31 and the finite temperature SEET and GF2 methods [32][33][34] are distinctively capable of directly obtaining the full frequencydependent spectra of the systems they model. Nevertheless, all of these methods struggle to balance computational cost with the need to account for the numerous electronic states that contribute to finite temperature expectation values.…”