dc.contributor.advisor Ting, Chin-Sen dc.creator Huang, Yixuan dc.date.accessioned 2020-06-04T04:08:10Z dc.date.created May 2020 dc.date.issued 2020-05 dc.date.submitted May 2020 dc.identifier.citation Portions of this document appear in: Huang, Yixuan, D. N. Sheng, and Chin-Sen Ting. "Charge density wave in a doped Kondo chain." Physical Review B 99, no. 19 (2019): 195109. And in: Huang, Yixuan, Xiao-yu Dong, D. N. Sheng, and C. S. Ting. "Global phase diagram and chiral spin liquids in the extended spin-$\frac {1}{2}$ honeycomb XY model." arXiv preprint arXiv:1912.11156 (2019). And in: Huang, Yixuan, Pavan Hosur, and Hridis K. Pal. "Deconstructing Magic-angle Physics in Twisted Bilayer Graphene with a Two-leg Ladder Model." arXiv preprint arXiv:2004.10325 (2020). dc.identifier.uri https://hdl.handle.net/10657/6732 dc.description.abstract The density matrix renormalization group method (DMRG) is a powerful numerical method for strongly correlated systems, which often cannot be solved analytically either by the mean field approach or through perturbation. The DMRG is originally proposed as an iterative search of the ground state in one dimension. With more researchers involving in the development of the algorithms based on DMRG, now it has become an optimized unbiased method for the strongly correlated problems. Compared with other numerical methods, the DMRG has one drawback that it cannot handle the lattices in three dimension. However, many materials with layered structure like the high-Tc superconductors can be approximated by the two dimensional lattice, and some models can be simplified or transformed into lower dimensions without losing information under certain situations. Here we have studied models of the electron systems in one dimension, and the spin systems in two dimension with large scale DMRG. For the Kondo lattice model we have found two charge-ordered phases in the doped regime which have not been found before. We also investigate the spin-$\frac{1}{2}$ XY model on the honeycomb lattice and identify a chiral spin liquid with additional chiral interactions. The chiral spin liquid has a non-trivial topological order with chiral edge states. Regarding the twisted bilayer graphene which is found experimentally to emerge a superconducting phase at low temperature, we construct an auxiliary model and provide insights to the exotic ferromagnetic Mott state that may exists in the twisted bilayer graphene. We also try to study the Kondo impurity problem in the presence of a superconductor and discuss the potential models with realistic interactions for future studies. dc.format.mimetype application/pdf dc.language.iso en dc.rights The author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. UH Libraries has secured permission to reproduce any and all previously published materials contained in the work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s). dc.subject strongly correlated system dc.subject numerical study dc.subject DMRG dc.title Density Matrix Renormalization Group Studies of Strongly Correlated Systems in Low Dimensions dc.date.updated 2020-06-04T04:08:11Z dc.type.genre Thesis thesis.degree.name Doctor of Philosophy thesis.degree.level Doctoral thesis.degree.discipline Physics thesis.degree.grantor University of Houston thesis.degree.department Physics, Department of dc.contributor.committeeMember Hosur, Pavan dc.contributor.committeeMember Ren, Zhifeng dc.contributor.committeeMember Bassler, Kevin E. dc.contributor.committeeMember Tsekos, Nikolaos V. dc.creator.orcid 0000-0003-1690-3354 local.embargo.terms 2022-05-01 local.embargo.lift 2022-05-01 dcterms.accessRights The full text of this item is not available at this time because the student has placed this item under an embargo for a period of time. The Libraries are not authorized to provide a copy of this work during the embargo period. dc.type.dcmi Text dc.format.digitalOrigin born digital dc.description.department Physics, Department of thesis.degree.college College of Natural Sciences and Mathematics
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