Atomic model of supersymmetric Hubbard operators

We apply the recently proposed supersymmetric Hubbard operators [P. Coleman, C. Pépin, and J. Hopkinson, Phys. Rev. B 63, 140411 (R) (2001)] to an atomic model. In the limiting case of free spins, we derive exact results for the entropy which are compared with a mean-field + Gaussian corrections description. We show how these results can be extended to the case of charge fluctuations and calculate exact results for the partition function, free energy, and heat capacity of an atomic model for some simple examples. Wave-functions of possible states are listed. We compare the accuracy of large N expansions of the susy spin operators [P. Coleman, C. Pépin, and A. M. Tsvelik, Phys. Rev. B 62, 3852 (2000); Nucl. Phys. B 586, 641 (2000)] with those obtained using "Schwinger bosons" and "Abrikosov pseudofermions." For the atomic model, we compare results of slave boson, slave fermion, and susy Hubbard operator approximations in the physically interesting but uncontrolled limiting case of N→2. For a mixed representation of spins, we estimate the accuracy of large N expansions of the atomic model. In the single box limit, we find that the lowest-energy susy saddle point reduces to simply either slave bosons or slave fermions, while for higher boxes this is not the case. The highest energy saddle point solution has the interesting feature that it admits a small region of a mixed-representation, which bears a superficial resemblance to that observed experimentally close to an antiferromagnetic quantum critical point.