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Zero modes of the Kitaev chain with phase-gradients and longer range couplings
Stockholm University, Faculty of Science, Department of Physics.ORCID iD: 0000-0002-9629-3594
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 22018 (English)In: Journal of Physics Communications, ISSN 2399-6528, Vol. 2, no 4, article id UNSP 045010Article in journal (Refereed) Published
Abstract [en]

We present an analytical solution for the full spectrum of Kitaev's one-dimensional p-wave superconductor with arbitrary hopping, pairing amplitude and chemical potential in the case of an open chain. We also discuss the structure of the zero-modes in the presence of both phase gradients and next nearest neighbor hopping and pairing terms. As observed by Sticlet et al, one feature of such models is that in a part of the phase diagram, zero-modes are present at one end of the system, while there are none on the other side. We explain the presence of this feature analytically, and show that it requires some fine-tuning of the parameters in the model. Thus as expected, these 'one-sided' zero-modes are neither protected by topology, nor by symmetry.

Place, publisher, year, edition, pages
2018. Vol. 2, no 4, article id UNSP 045010
Keywords [en]
Kitaev chain, zero Modes, cluster models
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-158175DOI: 10.1088/2399-6528/aab7e5ISI: 000434999300012OAI: oai:DiVA.org:su-158175DiVA, id: diva2:1234172
Available from: 2018-07-23 Created: 2018-07-23 Last updated: 2020-04-27Bibliographically approved
In thesis
1. Study of the phase diagram of Zn symmetric chains
Open this publication in new window or tab >>Study of the phase diagram of Zn symmetric chains
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study the phase diagrams of Zn symmetric chains. We start with investigating the topological phases of the Kitaev chain, a Z2 symmetric model, with long range couplings and a phase gradient. Then we go beyond the free fermion classification of topological phases and consider the effect of interactions by studying the Kitaev-Hubbard chain, incorporating a density-density interaction. Next we move on to the Z3 symmetric models and present a frustration free model with an exact three-fold degenerate ground state. In the end we present the phase diagram of a hopping model of Z3 Fock parafermions, the generalization of polarized Dirac fermions which could host at most two particles per site. The model has a pairwise hopping which is forbidden for fermions. In our studies we use analytical methods like the Lieb-Schultz-Mattis method, bosonization and conformal field theory, as well as numerical ones like exact diagonalization and the density matrix renormalization group.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2020. p. 117
National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-180941 (URN)978-91-7911-164-9 (ISBN)978-91-7911-165-6 (ISBN)
Public defence
2020-06-09, sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.

Available from: 2020-05-15 Created: 2020-04-22 Last updated: 2020-05-22Bibliographically approved

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