Wang, ZhiyuanHazzard, Kaden R.A.2018-07-162018-07-162018Wang, Zhiyuan and Hazzard, Kaden R.A.. "Analytic ground state wave functions of mean-fieldﾠpx+ipy superconductors with vortices and boundaries." <i>Physical Review B,</i> 97, no. 10 (2018) American Physical Society: https://doi.org/10.1103/PhysRevB.97.104501.https://hdl.handle.net/1911/102430We study Read and Green's mean-field model of the spinless px+ipy superconductor [N. Read and D. Green, Phys. Rev. B 61, 10267 (2000)] at a special set of parameters where we find the analytic expressions for the topologically degenerate ground states and the Majorana modes, including in finite systems with edges and in the presence of an arbitrary number of vortices. The wave functions of these ground states are similar (but not always identical) to the Moore-Read Pfaffian states proposed for the ν=5/2 fractional quantum Hall system, which are interpreted as the p-wave superconducting states of composite fermions. The similarity in the long-wavelength universal properties is expected from previous work, but at the special point studied herein the wave functions are exact even for short-range, nonuniversal properties. As an application of these results, we show how to obtain the non-Abelian statistics of the vortex Majorana modes by explicitly calculating the analytic continuation of the ground state wave functions when vortices are adiabatically exchanged, an approach different from the previous one based on universal arguments. Our results are also useful for constructing particle-number-conserving (and interacting) Hamiltonians with exact projected mean-field states.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlehttps://doi.org/10.1103/PhysRevB.97.104501