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We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra "Γ-term", using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, the low energy theory is described by an emergent SU(2)1 Wess-Zumino-Witten (WZW) model though the exact symmetry group is discrete. On the other hand, the relations between the local spin operators and the WZW currents and primary field contain SU(2) breaking coefficients. A modified nonabelian bosonization formula is proposed to capture such exotic emergent "partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an O h → D8 spontaneous symmetry breaking.

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Abstract. We investigate a quantum many-body system with particles moving on a circle and subject to two-body and three-body potentials. In this new class of models, that extrapolates from the celebrated Calogero-Sutherland model and a system with interactions among nearest and next-to-nearest neighbors, the interactions can be tuned as a function of range. We determine the exact ground state energy and wavefunction and obtain a part of the excitation spectrum.

A superconductor with px + ipy order has long fascinated the physics community because vortex defects in such a system host Majorana zero modes. Here we propose a simple construction of a chiral superconductor using proximitized quantum wires and twist angle engineering as basic ingredients. We show that a weakly coupled parallel array of such wires forms a gapless p-wave superconductor. Two such arrays, stacked on top of one another with a twist angle close to 90 • , spontaneously break time reversal symmetry and form a robust, fully gapped px + ipy superconductor. We map out topological phases of the proposed system, demonstrate existence of Majorana zero modes in vortices, and discuss prospects for experimental realization.