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Boundary phenomena and phase transitions in strongly correlated one dimensional systems
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Pasnoori, Parameshwar R.. Boundary phenomena and phase transitions in strongly correlated one dimensional systems. Retrieved from https://doi.org/doi:10.7282/t3-1599-m323

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TitleBoundary phenomena and phase transitions in strongly correlated one dimensional systems
NamePasnoori, Parameshwar R. (author); Andrei, Natan (chair); Vanderbilt, David (member); Zimmerman, Frank (member); Banks, Thomas (member); Azaria, Patrick (member); Rutgers University; School of Graduate Studies
Date Created2022
Other Date2022-10 (degree)
SubjectCondensed matter physics, Kondo effect, Majorana modes, Phase transitions, Superconductivity, Symmetry breaking, Topological phases
Extent1 online resource (334 pages) : illustrations
DescriptionOne dimensional quantum systems exhibit many interesting physical phenomena as a result of strong correlations. The gapped systems with symmetries exhibit exotic phases and are categorized as spontaneous symmetry breaking (SSB) or symmetry protected topological (SPT) phases. The systems with SSB such as the spin ½ XXZ chain have non vanishing local order parameter and a discrete symmetry is spontaneously broken leading to degenerate pairing in the spectrum. In contrast the systems with SPT such as charge conserving spin-triplet superconductors exhibit non-local order parameter and robust ground state degeneracy associated with protected fractionalized gapless excitations at the edges. In this work we consider one dimensional charge conserving superconductors and show that the SPT phases that arise not only depend on the bulk but rather it depends on the interplay of the bulk and the boundary conditions. We also show that the edge modes that arise in the system are robust to a certain extent against the boundary fields that break the symmetries protecting the SPT phase. We show that when the edges of a superconductor corresponding to a trivial phase are coupled to spin ½ quantum impurities, the system exhibits a very interesting phase structure, which arises due to the interplay between the Kondo effect and the bulk superconductivity. We consider the spin ½ antiferromagnetic XXZ chain in the gapped regime which exhibits SSB, and apply boundary fields which explicitly break the discrete symmetry which is spontaneously broken in the bulk. We find that the system exhibits a rich phase diagram and show that certain phases exhibit spin fractionalization associated with strong Majorana zero modes at the edges similar to the SPT phases. We then consider the isotropic XXX limit which corresponds to the Heisenberg spin chain, where the system becomes gapless and does not fall into either the SPT or SSB phases. We show that it exhibits a rich phase diagram and contains Majorana zero modes which arise at high energies. We show that in all the systems described above the Hilbert space is comprised of a certain number of towers of excited states, and they exhibit a new type of phase transition named Hilbert space or eigenstate phase transition where the number of towers of the Hilbert space changes.
NotePh.D.
NoteIncludes bibliographical references
Genretheses
Persistent URLhttps://doi.org/doi:10.7282/t3-1599-m323
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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