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Study of the phase diagram of Zn symmetric chains
Stockholm University, Faculty of Science, Department of Physics.ORCID iD: 0000-0002-9629-3594
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: urn:nbn:se:su:diva-180941ISBN: 978-91-7911-164-9 (print)ISBN: 978-91-7911-165-6 (electronic)OAI: oai:DiVA.org:su-180941DiVA, id: diva2:1425662
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At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.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
List of papers
1. Zero modes of the Kitaev chain with phase-gradients and longer range couplings
Open this publication in new window or tab >>Zero modes of the Kitaev chain with phase-gradients and longer range couplings
2018 (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.

Keywords
Kitaev chain, zero Modes, cluster models
National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-158175 (URN)10.1088/2399-6528/aab7e5 (DOI)000434999300012 ()
Available from: 2018-07-23 Created: 2018-07-23 Last updated: 2020-04-27Bibliographically approved
2. Exact results for a Z(3)-clock-type model and some close relatives
Open this publication in new window or tab >>Exact results for a Z(3)-clock-type model and some close relatives
2018 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 98, no 24, article id 245104Article in journal (Refereed) Published
Abstract [en]

In this paper, we generalized the Peschel-Emery line of the interacting transverse field Ising model to a model based on three-state clock variables. Along this line, the model has exactly degenerate ground states, which can be written as product states. In addition, we present operators that transform these ground states into each other. Such operators are also presented for the Peschel-Emery case. We numerically show that the generalized model is gapped. Furthermore, we study the spin-S generalization of interacting Ising model and show that along a Peschel-Emery line they also have degenerate ground states. We discuss some examples of excited states that can be obtained exactly for all these models.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-163557 (URN)10.1103/PhysRevB.98.245104 (DOI)000452003600011 ()
Available from: 2019-01-16 Created: 2019-01-16 Last updated: 2020-04-27Bibliographically approved
3. Study of the phase diagram of the Kitaev-Hubbard chain
Open this publication in new window or tab >>Study of the phase diagram of the Kitaev-Hubbard chain
2020 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 101, no 8, article id 085125Article in journal (Refereed) Published
Abstract [en]

We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbor density-density interaction, using both analytical techniques as well as DMRG. In the case of a moderate attractive interaction, the model has the same phases as the noninteracting chain, a trivial and a topological phase. For repulsive interactions, the phase diagram is more interesting. Apart from the previously observed topological, incommensurate, and charge density wave phases, we identify the excited state charge density wave phase. In this phase, the ground state resembles an excited state of an ordinary charge density phase, but is lower in energy due to the frustrated nature of the model. We find that the dynamical critical exponent takes the value z similar or equal to 1.8. Interestingly, this phase only appears for even system sizes, and is sensitive to the chemical potential on the edges of the chain. For the topological phase, we present an argument that excludes the presence of a strong zero mode for a large part of the topological phase. For the remaining region, we study the time dependence of the edge magnetization (using the bosonic incarnation of the model). These results further expand the region where a strong zero mode does not occur.

National Category
Physical Sciences
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-180419 (URN)10.1103/PhysRevB.101.085125 (DOI)000513583000006 ()
Available from: 2020-03-30 Created: 2020-03-30 Last updated: 2020-04-27Bibliographically approved
4. Phase diagram of the Z3 -Fock parafermion chain with pair hopping
Open this publication in new window or tab >>Phase diagram of the Z3 -Fock parafermion chain with pair hopping
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study a tight binding model of ℤ3-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge c=2, and two gapless phases with central charge c=1. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

National Category
Condensed Matter Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-180938 (URN)
Available from: 2020-04-21 Created: 2020-04-21 Last updated: 2020-04-27

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