Dresden 2020 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 33: Correlated Electrons: Method Development 1
TT 33.13: Talk
Wednesday, March 18, 2020, 12:45–13:00, HSZ 201
Wavefunctions for macroscopic electron systems — •Peter Fulde — Max-Planck-Institut für Physik komplexer Systeme
The dimensions of Hilbert space explode exponentially with number N of interacting electrons. Therefore, as stressed by W. Kohn [1], the concept of the many-electron wavefunction ψ (r1, …, rN) is in general not a legitimate scientific concept when N ≥ N0 where N0 is of order 103. The so called Exponential Wall Problem (EWP) does not exist though when the interactions are treated in a mean-field approximation, since then solving the Schrödinger equation reduces to a one-electron problem. It is easily seen that the EWP originates from the multiplicative form ψAB = ψA ⊗ ψB when two nearly coupled systems A and B are considered. This implies a high degree of information redundancy. In order to resolve the EWP when we want, e.g., to determine the electronic ground-state wavefunction of a periodic solid we have to find a representation in which the information redundancy is removed. It is shown how this is done and applied in practical calculations [2]. In essence the wavefunction is of a form corresponding to lnψ instead of ψ and therefore additive rather than multiplicative.
[1] W. Kohn: Rev. Mod. Phys. 71, 1253 (1999)
[2] P. Fulde: J. Chem. Phys. 150, 030901 (2019)