Generalized unitary Bogoliubov transformation that breaks fermion number parity

TL;DR

This paper introduces a generalized Bogoliubov transformation that breaks fermion number parity, allowing for continuous state variation between different fermion numbers, expanding the transformation's applicability beyond traditional parity-conserving cases.

Contribution

The authors develop a new variational form of the Bogoliubov transformation that can diagonalize Hamiltonians with broken fermion number parity, a capability not present in standard transformations.

Findings

Can diagonalize Hamiltonians with broken fermion parity

Does not lower energy for parity-conserving Hamiltonians

Enables continuous variation between states of different fermion numbers

Abstract

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.