  The two-particle self-consistent approach (TPSC) is a method for the one-band
Hubbard model that can be both numerically efficient and reliable. However,
TPSC fails to yield physical results deep in the renormalized classical regime
of the bidimensional Hubbard model where the spin correlation length becomes
exponentially large. We address the limitations of TPSC with improved
approaches that we call TPSC+ and TPSC+SFM. In this work, we show that these
improved methods satisfy the Mermin-Wagner theorem and the Pauli principle. We
also show that they are valid in the renormalized classical regime of the 2D
Hubbard model, where they recover a generalized Stoner criterion at zero
temperature in the antiferromagnetic phase. We discuss some limitations of the
TPSC+ approach with regards to the violation of the f-sum rule and conservation
laws, which are solved within the TPSC+SFM framework. Finally, we benchmark the
TPSC+ and TPSC+SFM approaches for the one-band Hubbard model in two dimensions
and show how they have an overall better agreement with available diagrammatic
Monte Carlo results than the original TPSC approach.
