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Boundaries of boundaries: A systematic approach to lattice models with solvable boundary states of arbitrary codimension
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 8, article id 085426Article in journal (Refereed) Published
Abstract [en]

We present a generic and systematic approach for constructing D−dimensional lattice models with exactly solvable d−dimensional boundary states localized to corners, edges, hinges, and surfaces. These solvable models represent a class of “sweet spots” in the space of possible tight-binding models—the exact solutions remain valid for any tight-binding parameters as long as they obey simple locality conditions that are manifest in the underlying lattice structure. Consequently, our models capture the physics of both (higher order) topological and nontopological phases as well as the transitions between them in a particularly illuminating and transparent manner.

Place, publisher, year, edition, pages
2019. Vol. 99, no 8, article id 085426
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-166152DOI: 10.1103/PhysRevB.99.085426ISI: 000459225100011OAI: oai:DiVA.org:su-166152DiVA, id: diva2:1289425
Available from: 2019-02-18 Created: 2019-02-18 Last updated: 2019-04-30Bibliographically approved
In thesis
1. Solvable Topological Boundaries
Open this publication in new window or tab >>Solvable Topological Boundaries
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The hallmark of topological phases of matter is the presence of robust boundary states. In this dissertation, a formalism is developed with which analytical solutions for these states can be straightforwardly obtained by making use of destructive interference, which is naturally present in a large family of lattice models. The validity of the solutions is independent of tight-binding parameters, and as such these lattices can be seen as a subset of solvable systems in the landscape of tight-binding models. The approach allows for a full control of the topological phase of the system as well as the dispersion and localization of the boundary states, which makes it possible to design lattice models possessing the desired topological phase from the bottom up. Further applications of this formalism can be found in the fields of higher-order topological phases—where boundary states localize to boundaries with a codimension larger than one—and of non-Hermitian Hamiltonians—which is a fruitful approach to describe dissipation, and feature many exotic features, such as the possible breakdown of bulk-boundary correspondence—where the access to exact solutions has led to new insights.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2019. p. 91
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-166135 (URN)978-91-7797-630-1 (ISBN)978-91-7797-631-8 (ISBN)
Public defence
2019-04-12, sal FB52, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 7: Submitted. Paper 8: Manuscript.

Available from: 2019-03-20 Created: 2019-02-22 Last updated: 2019-03-15Bibliographically approved

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