The TPSC+ approach: validity in the renormalized classical regime of the 2D Hubbard model*

The two-particle self-consistent approach (TPSC) is a non-perturbative approach for the Hubbard model. Though it satisfies local spin and charge sum rules, the Pauli principle, the Mermin-Wagner theorem and conservation laws, it overestimates spin fluctuations at low temperatures and is not valid deep in the renormalized classical regime of the 2D Hubbard model [1]. Recently, the TPSC+ approach was introduced as an improved version of the method [2]. In this work, we use analytical considerations to show that the TPSC+ approach is valid in the renormalized classical regime of the 2D Hubbard model, that it satisfies the Mermin-Wagner theorem and that it shows better self-consistency between one- and two-particle properties than the original TPSC approach. 

[1] Vilk, Y. M. et Tremblay, A.-M. S. J. Phys. I France 7, 1309–1368 (1997).

[2] Schäfer, T. et al. Phys. Rev. X 11, 011058 (2021).