Pairing and entanglement: quantum Monte Carlo studies

Described in this dissertation is the use of quantum Monte Carlo methods to study two ideas in quantum many-body problems: superfluidity and entanglement. Density matrices are presented a central tool in the analysis, as are discussed in the review of path integral Monte Carlo (PIMC) and variational Monte Carlo (VMC) methods. PIMC is used to model a one-dimensional system of fermionic lithium atoms according to existing experiments, including a realistic temperature. New estimators of the pair momentum distribution are implemented, yielding in a clear in-situ signature of a pairing mechanism (dubbed FFLO after its first proposers) which implies a microscopic phase fluctuation in space between a normal fluid and a superfluid. VMC is used to model homonuclear diatomic molecules of period-2 elements. The degree of entanglement and the responsible electronic configurations in real space are quantified in terms of the entanglement spectra. Calculating the reduced denstity matrix as an intermediate step reveals a novel way of understanding chemical bonds, as exemplified by Be2 and C2 . Possible implications of these results in integrable many-body models and in quantum chemistry are discussed, as well as direction for future investigation.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Yang, David Chang-Mo

Contributors dc:contributor

• Stone, Michael
• DeMarco, Brian L.
• Gollin, George D.
• Ceperley, David M.

• quantum Monte Carlo
• degenerate Fermi gas
• path integral Monte Carlo
• variational Monte Carlo
• quantum entanglement
• inhomogeneous superfluidity
• many-body correlation
• computational physics
• density matrix
• chemical bond
• one-dimensional system
• molecular physics

Statement dc:rights

• Copyright 2016 David Chang-Mo Yang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/90737

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/90737