Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model

Kyle Wamer
Event Date and Time: 
Tue, 2018-08-21 14:00 - 15:00
AMPEL #311
Local Contact: 
Ian Affleck

A lattice of interacting Majorana modes can occur in a superconducting film on a topological insulator in a magnetic field. The phase diagram as a function of interaction strength for the square lattice was analyzed recently using a combination of mean field theory and field theory and was found to include second order phase transitions. One of these corresponds to sponta- neous breaking of an emergent U(1) symmetry, for attractive interactions.

Despite the fact that the U(1) symmetry is not exact, this transition was claimed to be in a supersymmetric universality class when time reversal symmetry is present and in the conventional XY universality class when it is absent. Another second order transition was predicted for repulsive in- teractions with time reversal symmetry to be in the same universality class as the transition occurring in the Gross-Neveu model, despite the fact that the U(1) symmetry is not exact in the Majorana model. We analyze these phase transitions using the -expansion, and show that the emergent U(1) symmetry is not broken at either critical point. We also show that for a sufficiently weak fermion mass, supersymmetry remains at the transition for attractive interactions. When the fermion mass is large, the conventional XY transition is obtained.


Website development by Checkmark Media. Designed by Armada.

a place of mind, The University of British Columbia

Faculty of Science
Department of Physics and Astronomy
6224 Agricultural Road
Vancouver, BC V6T 1Z1
Tel 604.822.3853
Fax 604.822.5324

Emergency Procedures | Accessibility | Contact UBC | © Copyright The University of British Columbia