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On Aspects of Anyons and Quantum GraphsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Department of Physics, Stockholm University , 2017. , p. 107
##### National Category

Condensed Matter Physics
##### Research subject

Theoretical Physics
##### Identifiers

URN: urn:nbn:se:su:diva-142319ISBN: 978-91-7649-813-2 (print)ISBN: 978-91-7649-814-9 (electronic)OAI: oai:DiVA.org:su-142319DiVA, id: diva2:1092010
##### Public defence

2017-06-13, sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1209",{id:"formSmash:j_idt1209",widgetVar:"widget_formSmash_j_idt1209",multiple:true}); Available from: 2017-05-19 Created: 2017-04-28 Last updated: 2017-05-22Bibliographically approved
##### List of papers

This thesis consists of two distinct parts. The first part, based on the first two accompanied papers, is in the field of topological phases of matter and the second part, based on the third accompanied paper, looks at a problem in the field of quantum graphs, a rapidly growing field of mathematical physics.

First, we investigate the entanglement property of the Laughlin state by looking at the rank of the reduced density operator when particles are divided into two groups. We show that the problem of determining this rank translates itself into a question about symmetric polynomials, namely, one has to determine the lower bound for the *degree* in each variable of the symmetric polynomials that vanish under a transformation that clusters the particles into groups of equal size and then brings the particles in each group together. Although we were not able to prove this, but we were able to determine the lower bound for the *total* degree of symmetric polynomials that vanish under the transformation described. Moreover, we were able to characterize all symmetric polynomials that vanish under this transformation.

In the second paper, we introduce a one-dimensional model of interacting *su*(2)_{k }anyons. The specific feature of this model is that, through pairing terms present in the Hamiltonian, the number of anyons of the chain can fluctuate. We also take into account the possibility that anyons hop to empty neighboring sites. We investigate the model in five different points of the parameter space. At one of these points, the Hamiltonian of the model becomes a sum of projectors and we determine the explicit form of all the zero-energy ground states for odd values of *k*. At the other four points, the system is integrable and we determine the behavior of the model at these integrable points. In particular, we show that the system is critical and determine the CFT describing the system at these points.

It is known that there are non-Hermitian Hamiltonians whose spectra are entirely real. This property can be understood in terms of a certain symmetry of these Hamiltonians, known as *PT-*symmetry. It is also known that the spectrum of a non-Hermitian *PT*-symmetric Hamiltonian has reflection symmetry with respect to the real axis. We then ask the reverse question whether or not the reflection symmetry of a non-Hermitian Hamiltonian necessarily implies that the Hamiltonian is *PT*-symmetric. In the context of quantum graphs, we introduce a model for which the answer to this question is positive.

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isbn
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