Quadratic fermion Hamiltonian

A quadratic fermion Hamiltonian is bilinear in creation and annihilation operators. In a Majorana basis it is determined, up to a constant, by a real antisymmetric matrix.

Table of contents
- Bogoliubov--de Gennes Hamiltonian Quadratic fermion Hamiltonian
- Majorana fermion operator Quadratic fermion Hamiltonian
  - Majorana zero mode Majorana fermion operator

Bogoliubov--de Gennes Hamiltonian (BdG Hamiltonian)

 0  0

A Bogoliubov--de Gennes Hamiltonian acts on a Nambu particle-hole spinor and describes quadratic fermion hopping and pairing.

Majorana fermion operator

 0  0

A Majorana fermion operator is self-adjoint and obeys

{c_{j}, c_{k}} = 2 δ_{jk}

Majorana zero mode (MZM)

 0  0

A Majorana zero mode is a spatially localized Majorana operator that commutes with a gapped quadratic Hamiltonian, exactly or up to exponentially small finite-size corrections.