Superalgebraic solution to the mean-field Hubbard model

V. S. Kapitonov, P. A. Sevastyanov

Evgueny Kochetov, Marcin Mierzejewski

A simple version of the Bardeen-Cooper-Schrieffer (BCS)-type mean-field theory for the $t\ensuremath{-}J$ model is developed. The present approach rigorously treats the constraint of no doubly occupied states and invokes two local order parameters to implement spontaneous breaking of the global $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry. This is achieved by identifying the Hubbard operators with generators of the $\mathrm{SU}(2|1)$ superalgebra in the fundamental representation and employing the ensuing ${\mathrm{CP}}^{1|1}$ parametrization for dynamical variables. As a result, an improved phase diagram ${T}_{c}(\ensuremath{\delta})$ in the paramagnetic phase is obtained.

S. Marra, Francesco Paolo Mancini, A.M. Allega +1 more

Vladimir I. Anisimov, Yu. A. Izyumov

Nikolay M. Plakida, V. Yu. Yushankhaï

We show that the phase diagram and the odd p-wave quasiparticle gap for spinless fermions obtained in the paper by Kochetov and Mierzejewski for the $t\ensuremath{-}J$ model are artifacts of the adopted spin-charge separation treated in mean field approximation, while the critical remarks concerning the theory of exchange superconducting pairing derived within the Hubbard operator approach are misleading.

Elka Korutcheva