| dc.identifier.uri | http://hdl.handle.net/11401/76694 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Thesis | |
| dcterms.abstract | We discuss a short-range entangled topological phase in 3+1 dimensions that is pro- tected by time-reversal symmetry. Two models are compared that realize this phase: The first is a construction developed by Chen, Gu, Liu and Wen, which encodes the system’s topological properties in the representation of the symmetry group. The sec- ond theory uses a non-linear sigma model in which the distinct topological phases differ by the way the symmetry acts on the order parameter. Both theories have in common that the modeled phases are in one to one correspondence with the elements of the co- homology group H d+1 (Z T 2 , U T (1)). In this work, we extend the Chen-Gu construction to 3+1 dimensional systems. Furthermore, we show that both models coincide with re- spect to their topological properties. This is proved by comparing spin-flip processes and their associated topological phase factors. We derive spin-flip operators on the surface of the (3+1)-dimensional Chen-Gu construction that commute with time-reversal sym- metry. To implement spin-flip processes in the non-linear sigma model, we interpolate spin-configurations from a discrete, triangular lattice into the continuum. We proceed by analyzing the phases, generated by the θ-term, for spacetime configurations of the O(4) order parameter that correpond to these spin-flip processes. | |
| dcterms.abstract | We discuss a short-range entangled topological phase in 3+1 dimensions that is pro- tected by time-reversal symmetry. Two models are compared that realize this phase: The first is a construction developed by Chen, Gu, Liu and Wen, which encodes the system’s topological properties in the representation of the symmetry group. The sec- ond theory uses a non-linear sigma model in which the distinct topological phases differ by the way the symmetry acts on the order parameter. Both theories have in common that the modeled phases are in one to one correspondence with the elements of the co- homology group H d+1 (Z T 2 , U T (1)). In this work, we extend the Chen-Gu construction to 3+1 dimensional systems. Furthermore, we show that both models coincide with re- spect to their topological properties. This is proved by comparing spin-flip processes and their associated topological phase factors. We derive spin-flip operators on the surface of the (3+1)-dimensional Chen-Gu construction that commute with time-reversal sym- metry. To implement spin-flip processes in the non-linear sigma model, we interpolate spin-configurations from a discrete, triangular lattice into the continuum. We proceed by analyzing the phases, generated by the θ-term, for spacetime configurations of the O(4) order parameter that correpond to these spin-flip processes. | |
| dcterms.available | 2017-09-20T16:51:00Z | |
| dcterms.contributor | Fidkowski, Lukasz | en_US |
| dcterms.contributor | Schneble, Dominik | en_US |
| dcterms.contributor | Wei, Tzu-Chieh. | en_US |
| dcterms.creator | Dick, Sebastian Moritz | |
| dcterms.dateAccepted | 2017-09-20T16:51:00Z | |
| dcterms.dateSubmitted | 2017-09-20T16:51:00Z | |
| dcterms.description | Department of Physics. | en_US |
| dcterms.extent | 51 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76694 | |
| dcterms.issued | 2014-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:51:00Z (GMT). No. of bitstreams: 1
Dick_grad.sunysb_0771M_12420.pdf: 2355219 bytes, checksum: d25f0dee95aff0ab5a243327e888aa95 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Cohomology, Non-linear sigma model, Strongly correlated systems, Time-reversal symmetry, Topological insulator, Topology | |
| dcterms.subject | Physics | |
| dcterms.title | Analysis of short range entangled topological phases protected by time-reversal symmetry | |
| dcterms.type | Thesis | |
