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Stone, Michael DeMarco, Brian L. Gollin, George D. Yang, David Chang-Mo Ceperley, David M. 2016-07-07T20:27:06Z 2016-07-07T20:27:06Z 2018-07-08T09:15:23Z 2016-04-07 2016-05 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. Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01 The student, David Yang, accepted the attached license on 2016-04-05 at 03:00. The student, David Yang, submitted this Dissertation for approval on 2016-04-05 at 03:12. This Dissertation was approved for publication on 2016-04-07 at 13:32. DSpace SAF Submission Ingestion Package generated from Vireo submission #9148 on 2016-07-07 at 13:48:51 Made available in DSpace on 2016-07-07T20:27:06Z (GMT). No. of bitstreams: 3 YANG-DISSERTATION-2016.pdf: 4266618 bytes, checksum: 131d31a435d09494e4ee8a60e6a47992 (MD5) LICENSE.txt: 4207 bytes, checksum: a6782fad5d87032d6bd59f112aaf87fc (MD5) PROQUEST_LICENSE.txt: 4553 bytes, checksum: f0aaf30bf0b32b5b92c27f1ac1ad827e (MD5) Previous issue date: 2016-04-07 Embargo set by: Seth Robbins for item 93089 Lift date: 2018-07-07T20:28:14Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 93089 Lift date: 2018-07-07T20:35:34Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 93089 on 2018-07-08T09:15:23Z. application/pdf http://hdl.handle.net/2142/90737 en Copyright 2016 David Chang-Mo Yang 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 Pairing and entanglement: quantum Monte Carlo studies text text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.