Charged spin textures over the Moore–Read quantum Hall state

We study charged spin textures (CSTs) over the Moore–Read quantum Hall state at filling factor 5/2. We develop an algebraic framework and show that the pairing condition that is inherent in the Moore–Read state naturally leads to a class of CST, labeled by winding numbers [wI, wII]. The fundamental CSTs, with labels [1, 0] and electric charge e/4, is identified with the polar core vortex known in the spin-1 Bose–Einstein condensates literature. The spin texture carried by the fusion product of fundamental CSTs is correlated with the fusion channel of underlying non-Abelian quasiholes. Fractional quantum Hall (fqH) systems are the best-known realizations of topological order in nature. Among all observed fqH states, the one at ν = 5/2 is highly special. Its proposed theoretical descriptions, the Pfaffian (Moore–Read (MR)) [1] and anti-Pfaffian [2] states in particular, are based on a pairing mechanism and, as a consequence, admit excitations with non-Abelian braid statistics. In fqH systems, the magnetic and the Coulomb energies are of the same order and it is not a priori clear whether the electron spin plays a role in understanding these phases of matter. This leaves several possibilities. The first is that the ground state itself can be non-polarized. In a second possible scenario, the ground state is polarized, but the excitations involve overturned spins. In this paper, we analyze spin-full excitations over the MR state, which by itself is fully polarized. We analyze charged spin textures (CSTs) carrying the fundamental fractional charge q = e/4 and study the spin textures that arise upon fusing these excitations4. 3 Author to whom any correspondence should be addressed. 4 While our results are specific to the MR state, we expect that the essential insights carry over to a broader class of paired wave functions, such as the anti-Pfaffian state. New Journal of Physics 13 (2011) 045013 1367-2630/11/045013+09$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft