Pfaffian formula for fermion parity fluctuations in a superconductor and application to Majorana fusion detection. (English) Zbl 07760954
Summary: Kitaev’s Pfaffian formula equates the ground-state fermion parity of a closed system to the sign of the Pfaffian of the Hamiltonian in the Majorana basis. Using Klich’s theory of counting statistics for paired fermions, the Pfaffian formula is generalized to account for quantum fluctuations in the fermion parity of an open subsystem. A statistical description in the framework of random-matrix theory is used to answer the question when a vanishing fermion parity in a superconductor fusion experiment becomes a distinctive signature of an isolated Majorana zero-mode.
© 2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
© 2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
MSC:
| 81V74 | Fermionic systems in quantum theory |
| 82D55 | Statistical mechanics of superconductors |
| 15B52 | Random matrices (algebraic aspects) |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
Keywords:
circular ensembles; Majorana fermions; Majorana fusion rules; Majorana zero-modes; random determinants; random matrix theory; topological invariants; topological superconductivityReferences:
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