Friday, February 1, 2013

1301.7449 (Tarun Grover et al.)

A Lattice Model for Emergent Supersymmetry in D=2 Topological
Superconductors
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Tarun Grover, D. N. Sheng, Ashvin Vishwanath
A class of topological superconductors in two dimensions support gapless Majorana edge modes that are protected by time-reversal symmetry. Here we study the quantum phase transition (QPT) associated with the destruction of these edge modes as magnetic order develops spontaneously along the edge. It was recently conjectured that this quantum critical point has space-time supersymmetry, that emerges dynamically by tuning only one parameter. Here, we put this assertion to test by constructing a one-dimensional lattice model of the edge, in which the role of time reversal is played by a non-local symmetry. We solve this model using state-of-the-art Density Matrix Renormalization Group (DMRG) method, and indeed find emergent supersymmetry at the symmetry breaking transition. In particular, we find that the QPT lies in the tricritical Ising universality, even though it is generically accessible by tuning only one parameter. We provide a detailed description of the QPT, and discuss the consequences of the emergent supersymmetry.
View original: http://arxiv.org/abs/1301.7449

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