Entanglement and hall viscosity

This dissertation studies quantum entanglement in relation to the geometric response known as Hall viscosity. We begin by reviewing geometric response in the quantum Hall effect in comparison to its well-known electromagnetic response, Hall conductivity. We develop an understanding of momentum transport due to Hall viscosity in analogy to charge transport under Hall conductivity. We apply our momentum transport argument to continuum and lattice models of the quantum Hall effect. We also leverage this insight to reveal a previously-unrecognized manifestation of Hall viscosity: the acoustic Faraday effect in superfluid Helium-3 B. We suggest that the acoustic Faraday effect is a new platform for the direct observation of Hall viscosity in Helium-3 B and other systems. We then turn our focus to the entanglement spectrum. We calculate the momentum polarization of lattice models of the quantum Hall effect to determine the Hall viscosity based on the entanglement spectrum, revealing the close connection between geometric response and entanglement. Finally, we turn away from the quantum Hall effect to consider other topological insulators; we use the entanglement spectrum to develop a topological classification of composite systems comprising components of topological phases in different dimensions. Our composite topological index generalizes classification of weak and antiferromagnetic topological insulators. We predict the presence of topological bound states localized to defects in systems that are trivial under all other topological classifications.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Tuegel, Thomas

Contributors dc:contributor

• Hughes, Taylor L.
• Stone, Michael
• Vishveshwara, Smitha
• MacDougall, Gregory

• Quantum Hall effect
• Hall viscosity
• Superfluid Helium-3
• Entanglement
• Topological insulators

Statement dc:rights

• Copyright 2018 Thomas Tuegel

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101470

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101470