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Localized Majorana-like modes in a number conserving setting: An exactly solvable model

March 1, 2016 - 11:00am
Sebastian Diehl
University of Cologne
We discuss, in a number conserving framework, an exactly solvable model of interacting fermions supporting non-local zero-energy Majorana-like edge excitations. The construction draws intuition from an approach of targeted dissipative cooling into topologically non-trivial states. The model has an exactly solvable line, on varying the density of fermions, described by a topologically non-trivial ground state wave-function. Away from the exactly solvable line we study the system by means of the numerical density matrix renormalization group. We characterize its topological properties through the explicit calculation of a degenerate entanglement spectrum, establish the presence of a gap in its single particle spectrum while the Hamiltonian is gapless, and compute the correlations between the edge modes as well as the superfluid correlations. The exactly known ground state wavefunction allows us to construct analytically number conserving braiding operators, which are exponentially localized at the edges. 
PSC 2136
College Park, MD 20742