Helicity Modulus and Effective Hopping in the Two-Dimensional Hubbard Model Using Slave-Boson Methods

The slave-boson mean-field method is used to study the two-dimensional Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak- and strong ferromagnetism and antiferromagnetism, including all continuous and first-order transitions, is constructed and compared to the corresponding phase diagram using the Hartree-Fock approximation (HFA). Magnetically ordered regions are reduced by a factor of about 3 along both the $t/U$ and density axes compared to the HFA. Using the spin-rotation invariant formulation of the slave-boson method the helicity modulus is computed and for half-filling is found to practically coincide with that found using variational Monte Carlo calculations using the Gutzwiller wave function. Off half-filling the results can be used to compare with Quantum Monte Carlo calculations of the effective hopping parameter. Contrary to the case of half-filling, the slave-boson approach is seen to greatly improve the results of the HFA when off half-filling. (Submitted to: Journal of Physics: Condensed Matter)