Tuesday, May 28, 2013

1305.6270 (Stefano Chesi et al.)

Vortex Loops and Majorana Fermions    [PDF]

Stefano Chesi, Arthur Jaffe, Daniel Loss, Fabio L. Pedrocchi
We investigate the role that vortex loops play in characterizing eigenstates of certain systems of half-integer spins with nearest-neighbor interaction on a trivalent lattice. In particular we focus on ground states (and other low-lying states). We test our ideas on a "spin ladder" In certain cases we show how the vortex configuration of the ground state is determined by the relative signs of the coupling constants. Two methods yield exact results: i.) We utilize the equivalence of spin Hamiltonians with quartic interactions of Majorana fermions, and analyze that fermionic Hamiltonian. ii) We use reflection positivity for Majorana fermions to characterize vortices in ground states for reflection-symmetric couplings. Two additional methods suggest potential wider applicability of these results: iii.) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. iv.) A perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.
View original: http://arxiv.org/abs/1305.6270

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