Mixed-state topology and response

Mixed quantum states are ubiquitous in reality, and they can arise either from equilibrium systems at finite temperature, or from systems out of equilibrium. Similar to their zero-temperature counterparts, one can introduce the notion of topology for mixed quantum states. In this thesis, we study mixed state topology with special focus on its ensuing physical responses. This thesis consists of two parts. In the first part, we focus on finite-temperature equilibrium topological matter in two and three dimensions, and probe their topological thermal responses by coupling to background geometry, i.e., teleparallel gravity. For two-dimensional topological insulators at finite temperature, validness of the generalized Laughlin argument for thermal Hall effect remains controversial. We address this depute by deriving an effective action relying solely on fundamental symmetries, e.g., charge conservation, and time-translation symmetry (for equilibrium systems). We find that the ensuing effective action turns out to be a topological theta term associated with the background vielbein. This topological theta term has two salient features that resolve this puzzle: 1. It is invariant under variations up to boundary terms, so the thermal Hall current comes from edges; 2. It is gauge invariant, so there does not exist anomaly inflow, and the edge current is conserved, which further asserts the absence of Laughlin's argument for the thermal Hall effect. Also, we study the anomalous thermal Hall effect in three dimensional Weyl semimetals, in terms of teleparallel gravity. In the second part, we move to open quantum systems, where due to its coupling with environment, the detailed balance condition can be violated, pushing systems away from equilibrium. Despite quantized topological invariants can be defined, possible physical responses probing underlying topology remain largely obscure. In this part, to provide an unified organizing principle, we derive an effective action for mixed quantum states in the long-time limit in all dimensions and demonstrate its independence of the underlying equilibrium or non-equilibrium nature of dynamics. This action not only possesses non-quantized linear responses, but more importantly, also quantized non-linear responses that are measurable by interferometric experiments or full counting statistics. Quantization of these non-linear responses is inherited from underlying topology invariants of mixed quantum states, representing new experimental signatures for non-equilibrium topological phases of matter. Also, dimensional reduction of our effective action naturally yields non-linear responses for descendant states in lower dimensions, enabling us to classify mixed quantum states in different dimensions.

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

2022

Author dc:creator

• Huang, Zemin

Contributors dc:contributor

• Stone, Michael
• Bradlyn, Barry
• Cooper, Stephen Lance
• Noronha, Jorge Leite

• Mixed Quantum State
• Topological Quantum Matter
• Open Quantum System

Statement dc:rights

• Copyright 2022 Ze-Min Huang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/117628

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F117628