Page 1 |
Save page Remove page | Previous | 1 of 96 | Next |
|
small (250x250 max)
medium (500x500 max)
large ( > 500x500)
Full Resolution
All (PDF)
|
This page
All
Subset |
Object Description
| Title | Entanglement in quantum critical and topological phases |
| Author | Ding, Letian |
| Author email | letiand@usc.edu; letiandi@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Physics |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2010-05-28 |
| Date submitted | 2010 |
| Restricted until | Unrestricted |
| Date published | 2010-06-23 |
| Advisor (committee chair) | Haas, Stephan |
| Advisor (committee member) |
Bickers, Nelson Nakano, Aiichiro Däppen, Werner Zhang, Jianfeng |
| Abstract | In this dissertation, we studied quantum entanglement in the context of many-body physics. Based on quasi-free bipartite fermionic models, we were able to study the entanglement entropy and its spectrum in various quantum phases. Particularly, we studied the p wave superconducting paring states, which contain quantum critical phases with different Fermi surface topology, and we also studied the px+ ipy wave superconducting paring states, which contain not only quantum critical phases but also quantum topological phases.; In the p wave superconducting states, we investigated the scaling behavior of entanglement entropy of a general quadratic fermionic Hamiltonian in higher dimensions. The three distinguished phases in these systems are a non-critical phase, a critical phase with a finite Fermi surface and a critical phase with only nodal fermion points. With the help of exact diagonalization, we were able to calculate the entanglement entropy with a very high precision. In non-critical states we found that the area law indeed holds, and logarithmic corrections to the area law are present in critical states with a finite Fermi surface. For critical states with only nodal Fermi points, we found that the logarithmic corrections to the area law are absent.; We also worked out a bound of the entanglement entropy for a generic bipartite fermion system using an analytic method. It was found that for states with a finite Fermi surface, the entanglement entropy in the system shows violation of the area law with a logarithmic correction. And for other critical systems and the fully gapped systems, the lower bound of the block entropy still obeys an area law. Our study gives clear evidence that the relationship between entanglement and correlations in higher dimensional systems is different than in d=1, and that a crucial role is played by the geometry of the Fermi surface.; In the px+ ipy wave superconducting paring states,we investigated topological order with parity and time-reversal symmetry breaking. Large-scale numerical calculations of the entanglement spectrum and entanglement entropy reveal universal behavior in these systems. In particular, we found a chiral, gapless Majorana fermion excitation in the entanglement spectrum of the weak-pairing phase, and contrasted this with the gapped spectrum in the strong-pairing phase. A variety of topological phases can be described by a pairing Hamiltonian that neglects order parameter fluctuations. Our studies also confirmed the corner effects in the sub-leading term of the entanglement entropy. Additional to entanglement entropy, we also found that the entanglement spectrum provides an alternative robust way to detect and characterize non-Abelian topological order in the ground-state wavefunction of such phases. We found in non-Abelian topological phases, the power-law decay of the lowest eigenvalue in the entanglement spectrum carries the information for the hidden order in the system. |
| Keyword | entanglement entropy; entanglement spectrum; quantum criticality; quantum entanglement; topological phases |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3149 |
| Rights | Ding, Letian |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Ding-3837 |
| Archival file | uscthesesreloadpub_Volume17/etd-Ding-3837.pdf |
Description
Comments
Post a Comment for Page 1
