White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Diagnosing Topological Quantum Matter via Entanglement Patterns

Meichanetzidis, Konstantinos (2017) Diagnosing Topological Quantum Matter via Entanglement Patterns. PhD thesis, University of Leeds.

[img]
Preview
Text
Meichanetzidis_K_Mathematics-Physics_PhD_2017.pdf - Final eThesis - complete (pdf)
Available under License Creative Commons Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales.

Download (16Mb) | Preview

Abstract

Quantum matter involves the study of entanglement patterns in the ground states of many-body systems. Of significant interest have recently been topological states of matter, which exhibit characteristics only described globally. As such they are robust to local deformations. In this thesis, we study inter-correlations of many-body states through the entanglement spectrum, obtained by a bipartition of both topological and non-topological systems. In particular, we introduce two novel diagnostics which operate on entanglement spectra. For topological phases supporting edge states on open boundaries we take a quantum-information inspired approach by invoking the monogamy relations obeyed by multi-partite systems. Within a strictly single-particle framework, we establish a correspondence between highly entangled mode and the existence of edge states. In the many-body context, we introduce the interaction distance of a mixed state. Exclusively via the entanglement spectrum it determines how close a free-fermion state lies and what the emergent free quasiparticles are. We apply these two measures to diagnose the properties of a variety of free and interacting fermionic topological systems and reinterpret their properties from a fresh point of view. Our case studies revolve around Kitaev's honeycomb model, which supports both short-range and long-range topological order, constituting it thus relevant to both the monogamy qualifier and the interaction distance. The possibility to diagnose whether a model has zero interacting distance or if it supports maximally entangled states provides central and compact information about the behaviour of complex quantum systems.

Item Type: Thesis (PhD)
Related URLs:
Keywords: Quantum Matter, Quantum Information, Entanglement
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Identification Number/EthosID: uk.bl.ethos.729444
Depositing User: Dr Konstantinos Meichanetzidis
Date Deposited: 07 Dec 2017 12:35
Last Modified: 25 Jul 2018 09:56
URI: http://etheses.whiterose.ac.uk/id/eprint/18806

You do not need to contact us to get a copy of this thesis. Please use the 'Download' link(s) above to get a copy.
You can contact us about this thesis. If you need to make a general enquiry, please see the Contact us page.

Actions (repository staff only: login required)