Emergent topological properties in one-dimensional metals
I consider interacting multi-channel one-dimensional systems with gapless charge excitations but with gaps in the neutral sector. For the case of two channels, I will illustrate that there are two-distinct ground state phases, one of which has an emergent topology protected by time-reversal symmetry. This emergent topological phase has fractionalised zero-energy Majorana modes localised at the ends of the system. I will discuss various models that potentially realise such a phase, and will also consider show that the ground state phase is robust to impurities and/or disorder, as well as talking about various crossovers that may take place at higher temperature. I will then discuss the case of three channels, where I will demonstrate a realisation of a parafermion topological phase, protected by a Z3 symmetry. In this case, the Z3 symmetry itself is also emergent and is not required to be present in the original Hamiltonian.
References:
N. Kainaris, S. T. Carr, Physical Review B 92 (3), 035139 (2015)
R. A. Santos, D. B. Gutman, S. T. Carr, Physical Review B 93 (23), 235436 (2016)
N. Kainaris, R. A. Santos, D. B. Gutman, S. T. Carr, Fortschritte der Physik 65 (6-8) (2017)
N. Kainaris, S. T. Carr, A. D. Mirlin, Physical Review B 97 (11), 115107 (2018)
R. A. Santos, D. B. Gutman, S. T. Carr, arXiv:1805.10045 (2018)