| dc.identifier.uri | http://hdl.handle.net/11401/76666 | |
| 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 | Dissertation | |
| dcterms.abstract | The classical simulation of many-body quantum systems is an essential tool in understanding many fundamental aspects of condensed matter physics. But a major obstacle arises from the number of degrees of freedom involved in describing such systems, which is exponential in the system size. Recently, however, a class of numerical techniques based on structures called "tensor networks" has emerged, which allows many "typical" quantum states (such as the ground states of gapped, local Hamiltonians) to be represented much more efficiently. In this work we extend and apply these techniques to consider several central topics in quantum many-body physics. After reviewing the relevant background material from the field of tensor networks and tensor network states, we demonstrate a method for computing high order moments and cumulants of operators with respect to such states, including the so-called "Binder cumulant," a powerful tool for detecting phase transitions. Next, we employ tensor network algorithms to characterize the ground state phase diagram of a quantum spin model, including both symmetry-breaking phases and symmetry protected topological order, and find a signicant variety of phases and phase transitions. Finally, we consider the entanglement properties of quantum states exhibiting many-body localization, using a combination of exact diagonalization and tensor network techniques. | |
| dcterms.available | 2017-09-20T16:50:55Z | |
| dcterms.contributor | Wei, Tzu-Chieh | en_US |
| dcterms.contributor | Fidkowski, Lukasz | en_US |
| dcterms.contributor | Schneble, Dominik | en_US |
| dcterms.contributor | Ganeshan, Sriram. | en_US |
| dcterms.creator | West, Colin Gareth | |
| dcterms.dateAccepted | 2017-09-20T16:50:55Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:55Z | |
| dcterms.description | Department of Physics | en_US |
| dcterms.extent | 231 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76666 | |
| dcterms.issued | 2016-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:55Z (GMT). No. of bitstreams: 1
West_grad.sunysb_0771E_12809.pdf: 6417350 bytes, checksum: 8b47716f0dff0610df929f4847278579 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Binder Cumulant, Many Body Localization, Matrix Product State, Phase Transition, Symmetry-Protected Topological, Tensor Network | |
| dcterms.subject | Quantum physics -- Condensed matter physics -- Theoretical physics | |
| dcterms.title | Applications of Tensor Network Algorithms in Quantum Many-Body Physics | |
| dcterms.type | Dissertation | |
