# Mapping the braiding properties of the Moore-Read state - Condensed Matter > Strongly Correlated Electrons

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Abstract: In this paper we explore the braiding properties of the Moore-Read fractionalHall sequence, which amounts to computing the adiabatic evolution of the Hallliquid when the anyons are moved along various trajectories. In this work, theanyons are pinned to precise spatial configurations by using specific externalpotentials. Such external potentials break the translational symmetry and itappears that one will be forced to simulate the braidings on the entiremany-body Hilbert space, an absolutely prohibitive scenario. We demonstrate howto overcome this difficulty and obtain the exact braidings for fairly largeHall systems. For this, we show that the incompressible state of a general$k,m$ fractional Hall sequence can be viewed as the unique zero mode of aspecific Hamiltonian $H^{k,m}$, whose form is explicitly derived by usingk-particles creation operators. The compressible Hall states corresponding to$n$$\times$$k$ anyons fixed at $w 1$,

.,$w {nk}$ are shown to be the zeromodes of a pinning Hamiltonian $H^{k,m} {w 1, .,w {nk}}$, which is alsoexplicitly derived. The zero modes of $H^{k,m} {w 1, .,w {nk}}$ are shown tobe contained in the space of the zero modes of $H^{k,m}$. Therefore, thecomputation of the braidings can be done entirely within this space, which wemap out for a number of Hall systems. Using this efficient computationalmethod, we study various properties of the Moore-Read states. In particular, wegive direct confirmation of their topological and non-abelian properties thatwere previously implied from the underlying Conformal Field Theory CFTstructure of the Moore-Read state.

Autor: Emil Prodan, F.D.M. Haldane

Fuente: https://arxiv.org/