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We investigate the effect of repulsive and attractive onsite interactions on a Quantum Spin Hall Insulator (QSHI). For repulsive interactions, we show that the topological phase is stable up to quite large interactions U ~ t before the system reaches a magnetically ordered phase [1]. For attractive interactions, we discuss superconductivity in a doped QSHI and compare it with a doped trivial band insulator. We also consider the effect of spin orbit coupling to zero-mode bound states at a vortex core.
As examples of symmetry protected phases in one dimension, we consider a spin 2 chain exhibiting two topologically distinct phases [2] whose properties are discussed. Eventually, we derive the effective conformal theory of the (topological) quantum phase transition between the phases.
[1] S. Rachel and K. Le Hur, Phys. Rev. B 82, 075106 (2010). [2] H.-C. Jiang, S. Rachel, Z.-Y. Weng, S.-C. Zhang, and Z. Wang, arXiv:1010.4273. |
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