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Excited States in Variational Many-Body Approaches

Gustafsson, David LU (2018) PHYM01 20181
Mathematical Physics
Department of Physics
Abstract
A method is implemented wherein numerical approximations to the ground
and first few excited states of a quantum mechanical N -body 1D harmonic
oscillator are found through variational methods, representing the states as a
linear combination of normalized pseudo-states which are themselves linear
combinations of non-orthogonal Slater determinants. These states are then
used as a low energy basis for configuration interaction. An expression is
derived for an analytical matrix derivative of the energy functional, in order
to improve the speed of the variation.
The speed and accuracy using the analytical derivative is compared to
that of the numerical derivative, and a number of different gradient descent
methods are tried and... (More)
A method is implemented wherein numerical approximations to the ground
and first few excited states of a quantum mechanical N -body 1D harmonic
oscillator are found through variational methods, representing the states as a
linear combination of normalized pseudo-states which are themselves linear
combinations of non-orthogonal Slater determinants. These states are then
used as a low energy basis for configuration interaction. An expression is
derived for an analytical matrix derivative of the energy functional, in order
to improve the speed of the variation.
The speed and accuracy using the analytical derivative is compared to
that of the numerical derivative, and a number of different gradient descent
methods are tried and compared. (Less)
Please use this url to cite or link to this publication:
author
Gustafsson, David LU
supervisor
organization
course
PHYM01 20181
year
type
H2 - Master's Degree (Two Years)
subject
keywords
quantum mechanics, many-body problems, excited states, Hartree-Fock method, variational method, VAMPIR
language
English
id
8963534
date added to LUP
2018-12-18 14:13:13
date last changed
2018-12-18 14:13:13
@misc{8963534,
  abstract     = {{A method is implemented wherein numerical approximations to the ground
and first few excited states of a quantum mechanical N -body 1D harmonic
oscillator are found through variational methods, representing the states as a
linear combination of normalized pseudo-states which are themselves linear
combinations of non-orthogonal Slater determinants. These states are then
used as a low energy basis for configuration interaction. An expression is
derived for an analytical matrix derivative of the energy functional, in order
to improve the speed of the variation.
The speed and accuracy using the analytical derivative is compared to
that of the numerical derivative, and a number of different gradient descent
methods are tried and compared.}},
  author       = {{Gustafsson, David}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Excited States in Variational Many-Body Approaches}},
  year         = {{2018}},
}