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Many-body-based DFT treatment of fermions in optical lattices

Westergren, Jérémie LU (2017) FYSK02 20171
Department of Physics
Mathematical Physics
Abstract
With recent advances in the field of ultra cold atoms one can, by trapping atoms
at low temperatures by laser beams, simulate systems which can be adequately
described by single-band lattice Hamiltonians. Also, due to the high parameter
tunability of the experimental setups, lattice disorder can be introduced in a con-
trolled fashion in these systems. This thesis considers disordered/ordered interacting
fermion lattice systems in equilibrium in one and two dimensions, subject to trap-
ping parabolic potentials, where different levels of description, ranging from exact
where possible (in 1D, Density Matrix Renormalization Group, DMRG), to approxi-
mate (based on several local-density approximations within the framework of Lattice
... (More)
With recent advances in the field of ultra cold atoms one can, by trapping atoms
at low temperatures by laser beams, simulate systems which can be adequately
described by single-band lattice Hamiltonians. Also, due to the high parameter
tunability of the experimental setups, lattice disorder can be introduced in a con-
trolled fashion in these systems. This thesis considers disordered/ordered interacting
fermion lattice systems in equilibrium in one and two dimensions, subject to trap-
ping parabolic potentials, where different levels of description, ranging from exact
where possible (in 1D, Density Matrix Renormalization Group, DMRG), to approxi-
mate (based on several local-density approximations within the framework of Lattice
Density Functional Theory) are used. The exchange-correlation potentials consid-
ered come from Many-Body Approximations obtained using Green’s functions, as
well as from an exact local-density approximation (LDA) based on the Bethe-Ansatz
(BALDA) in 1D. Both one- and two-dimensional systems were studied in equilib-
rium, essentially looking at the ground state density profiles. Furthermore, in 2D,
a pseudo-dynamics representing the trap-opening in the complete adiabatic limit
was also studied. For one-dimensional systems, it is found that, in general, BALDA
yields very good results compared to DMRG, except for the low density limit, but
DMRG can describe features that none of the LDA:s considered can reproduce. It
is also found that the strength of the external potential affects the impact that the
exchange-correlation potential has on the system. Many of these features translate
to the 2D case. However, a new aspect emerges in two dimensions, related to the
competition of disorder and interaction. Here an important outcome is that, on
opening the trap at an ideally adiabatic rate, different MBA:s (and thus different
LDA:s) provide different minimal vs maximal expansion radii of the particle cloud, as
a result of the interplay of disorder and interaction, and the underlying square lattice
structure. For the 2D results, exact benchmarks were not available, and our findings
may thus need further validation, by e.g. considering several disorder configurations
or, ideally, by performing full Green’s function calculations. These considerations
are summarised in our conclusions and outlook remarks, where possible directions
for future investigation are highlighted. (Less)
Please use this url to cite or link to this publication:
author
Westergren, Jérémie LU
supervisor
organization
course
FYSK02 20171
year
type
M2 - Bachelor Degree
subject
keywords
DFT, density functional theory, MBA, many-body approximations, Hubbard model, Ultra cold atoms, cold atoms, optical lattice
language
English
id
8915142
date added to LUP
2017-06-14 17:07:00
date last changed
2017-06-14 17:07:00
@misc{8915142,
  abstract     = {With recent advances in the field of ultra cold atoms one can, by trapping atoms
at low temperatures by laser beams, simulate systems which can be adequately
described by single-band lattice Hamiltonians. Also, due to the high parameter
tunability of the experimental setups, lattice disorder can be introduced in a con-
trolled fashion in these systems. This thesis considers disordered/ordered interacting
fermion lattice systems in equilibrium in one and two dimensions, subject to trap-
ping parabolic potentials, where different levels of description, ranging from exact
where possible (in 1D, Density Matrix Renormalization Group, DMRG), to approxi-
mate (based on several local-density approximations within the framework of Lattice
Density Functional Theory) are used. The exchange-correlation potentials consid-
ered come from Many-Body Approximations obtained using Green’s functions, as
well as from an exact local-density approximation (LDA) based on the Bethe-Ansatz
(BALDA) in 1D. Both one- and two-dimensional systems were studied in equilib-
rium, essentially looking at the ground state density profiles. Furthermore, in 2D,
a pseudo-dynamics representing the trap-opening in the complete adiabatic limit
was also studied. For one-dimensional systems, it is found that, in general, BALDA
yields very good results compared to DMRG, except for the low density limit, but
DMRG can describe features that none of the LDA:s considered can reproduce. It
is also found that the strength of the external potential affects the impact that the
exchange-correlation potential has on the system. Many of these features translate
to the 2D case. However, a new aspect emerges in two dimensions, related to the
competition of disorder and interaction. Here an important outcome is that, on
opening the trap at an ideally adiabatic rate, different MBA:s (and thus different
LDA:s) provide different minimal vs maximal expansion radii of the particle cloud, as
a result of the interplay of disorder and interaction, and the underlying square lattice
structure. For the 2D results, exact benchmarks were not available, and our findings
may thus need further validation, by e.g. considering several disorder configurations
or, ideally, by performing full Green’s function calculations. These considerations
are summarised in our conclusions and outlook remarks, where possible directions
for future investigation are highlighted.},
  author       = {Westergren, Jérémie},
  keyword      = {DFT,density functional theory,MBA,many-body approximations,Hubbard model,Ultra cold atoms,cold atoms,optical lattice},
  language     = {eng},
  note         = {Student Paper},
  title        = {Many-body-based DFT treatment of fermions in optical lattices},
  year         = {2017},
}