On the nature of “strong” Bogoliubov transformations for fermions

Sergio Caracciolo A, F. Palumbo, Giovanni Viola

M. Iwasaki

We study the improper Bogoliubov transformation which is an improper rotation in the SO(2N) group in Fermion systems. The mathematical properties of the Bogoliubov transformation are investigated generally, when the dimension N is odd. It is shown that the improper transformation appears naturally and some quasi-particles become gapless. This leads to the property that some physical quantities have singularities in momentum space across the Fermi surface. Moreover it is pointed out that such a case may be realized in quark matter.

Raoelina Andriambololona

Paweł Caban, Krzysztof Podlaski, Jakub Rembieliński +2 more

We show that Bogoliubov transformations, widely used in quantum field theory, can be also useful in quantum information theory. Namely, we show that the problem of the choice of tensor product decomposition in the system of two fermions can be analysed with the help of Bogoliubov transformations of creation and annihilation operators.

Wolfgang Witschel

Jonathan E. Moussa

The standard Bogoliubov transformation is generalized to enable fermion number parity breaking. The new transformation can diagonalize fermion Hamiltonians that are quadratic in fermion and number parity operators. This new variational freedom cannot lower the energy of Hamiltonians that conserve number parity. However, it has value as a minimal mechanism for continuously varying between states of different fermion number, regardless of number parity.