Feder, David L.Cameron, Alexander Carlo2019-10-092019-10-092019-10-08Cameron, A. C. (2019). Quantum Phase Characterization via Entanglement Scaling in Fermionic Quantum Wires (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/111147Quantum entanglement is studied in the context of its use as a probe of quantum phases within fermionic non-interacting quantum wires. In particular, we consider the uniform lattice, as well as the Su-Schreiffer-Heeger (SSH) model, and use the bipartite entropy of entanglement to characterize their quantum phases. In 1D, it has been shown analytically that the von Neumann entropy defined for a subsystem $\mathcal{H}_A \subset \mathcal{H}_A\otimes\mathcal{H}_B$ takes distinct forms dependent on the whether or not the state is thermodynamically gapped. It is also known that entanglement can be used to identify topological phases of a quantum system, such as the symmetry protected phase found in the SSH model. These results are confirmed numerically, and some common techniques for the calculation of bipartite entanglement are compared according to their aptitude for simulating larger and more complicated systems.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.EntanglementFermionsQuantum PhaseEducation--SciencesPhysicsCondensed MatterPhysics--Theorymaster thesis10.11575/PRISM/37205