Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

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Séminaire de groupe

Long-range Kitaev model: phases, correlations and edge modes
Davide Vodola
Equipe 106, Institut Jean Lamour
jeudi 31 mars 2016 , 10h25
Salle de séminaire du groupe de Physique Statistique

We analyze the quantum phases, correlation functions and edge modes for a class of fermionic superconducting Hamiltonians that generalise the Kitaev chain,where pairing terms are long-range and decay with distance as a power-law. We provide the phase diagram based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur also in gapped regions, while connected correlation functions can decay with a hybrid exponential and power-law behaviour. Along the critical lines, breaking of conformal symmetry is also found. For finite values of the decay exponent of the pairing, we show that the two Majorana massless fermions (arising in the short-range limit as edge modes) can acquire a mass and get paired together into a massive non-local Dirac fermion localised at both edges of the chain. We argue that this phase is topological and has fractional topological numbers as a consequence of the long-range couplings.

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