PIRSA:11100074

Topological Liquid Nucleation Induced by Vortex-vortex Interactions in Kitaev's Honeycomb Model

Lahtinen, V. (2011). Topological Liquid Nucleation Induced by Vortex-vortex Interactions in Kitaev's Honeycomb Model. Perimeter Institute. https://pirsa.org/11100074

Lahtinen, Ville. Topological Liquid Nucleation Induced by Vortex-vortex Interactions in Kitaev's Honeycomb Model. Perimeter Institute, Oct. 26, 2011, https://pirsa.org/11100074 

          @misc{ pirsa_PIRSA:11100074,
            doi = {10.48660/11100074},
            url = {https://pirsa.org/11100074},
            author = {Lahtinen, Ville},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Topological Liquid Nucleation Induced by Vortex-vortex Interactions in Kitaev{\textquoteright}s Honeycomb Model},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {oct},
            note = {PIRSA:11100074 see, \url{https://pirsa.org}}
          }

Ville Lahtinen

Nordita - Nordic Institute for Theoretical Physics

Talk number
PIRSA:11100074
Collection
Talk Type
Subject
Abstract
We provide a microscopic understanding of the nucleation of topological quantum liquids that arise due to interactions between non-Abelian anyons. With the pairwise anyon interactions typically showing RKKY-type oscillations in sign, but decaying exponentially with distance, we show that the character of the nucleated phase is fully determined by anyon interactions beyond nearest neighbor exchange. We investigate this issue in the context of Kitaev's honeycomb lattice model. In the presence of vortex lattices, depending on microscopic parameters such as the vortex lattice spacing, we observe the nucleation of several distinct Abelian topological phases, that differ in their band structure and Chern number description. By employing an effective model of Majorana fermions, we show that these phases can be fully predicted from the vortex-vortex interactions. Corresponding microscopic results should hold for vortices forming an Abrikosov lattice in a p-wave superconductor or quasiholes forming a Wigner crystal in non-Abelian quantum Hall states.