Product wave-functions in Fock-space
Product wave-functions in Fock-space
Slater determinants provide a convenient basis for expanding many-electron wave functions. In second quantization they are written as a product of creation operators acting on the vacuum. While it is possible to self-consistently determine the Salter determinant that minimizes the energy expectation...
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Personal Name(s): | Thi, Hoai Le (Corresponding author) |
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Contributing Institute: |
GRS; GRS |
Imprint: |
2015
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Physical Description: |
82 p. |
Dissertation Note: |
RWTH Aachen, Masterarbeit, 2015 |
Document Type: |
Master Thesis |
Research Program: |
Computational Science and Mathematical Methods |
Subject (ZB): | |
Link: |
OpenAccess OpenAccess |
Publikationsportal JuSER |
Slater determinants provide a convenient basis for expanding many-electron wave functions. In second quantization they are written as a product of creation operators acting on the vacuum. While it is possible to self-consistently determine the Salter determinant that minimizes the energy expectation value, the resulting Hartree-Fock wave function does not contain any correlations. For this we need to consider linear combinations of Slater determinants. Working in Fock space we can produce many-electron states containing correlations while still maintaining the simple product form of the wave function: Introducing Bogoliubov operators that mix electron creation and annihilation operators, we can form second-quantized operators with the same algebraic properties as the ordinary creation and annihilation operators. Product-states of these Bogoliubov operators are many-electron wave functions for which the number of electrons is not fixed. Projected to an N-electron Hilbert space they are given by linear combinations of Slater determinants. The simplest example is the BCS wave function for superconducting systems. We derive the self-consistent Hartree-Fock-Bogoliubov equations for finding the best Fock-space product state, implement them numerically and analyze the quality of the resulting wave functions for a number of simple model systems. |