Generalized Bogoliubov-Hartree-Fock Theory - Magnetic order and superconductivity in extended Hubbard models

We present a generalized Bogoliubov-Hartree-Fock theory, which allows to study magnetic ordering, charge ordering, and superconductivity on the same footing and gives additional information about the so-called mixed phases [1]. These phases emerge in parameter ranges where the system is potentially strongly affected by fluctuations and cannot be described by any set of usual Hartree-Fock states (Slater determinants) [1,2]. Furthermore, we show how to obtain the self-consistent set of order parameters in the normal and BCS states by straightforward unrestricted global minimization of the appropriate Landau functional [3]. This method allows us to study the coexistence and competition of various magnetic and superconducting order and can be used to study the possibility of additional phase transitions in the coexistence regime.

[1] E. Langmann and M. Wallin, J. Stat. Phys. 127, 825 (2007)
[2] V. Bach et al., J. Stat. Phys. 76, 3 (1994)
[3] R. Agra et al., Eur. J. Phys. 27, 407 (2006)