Weyl semimetallic, Néel, stripe, and vortex states in the Rashba-Hubbard model.

We investigate the evolution of magnetic phases in the Hubbard model under strong Rashba spin-orbit coupling on a square lattice. By combining Lanczos exact diagonalization with Determinant Quantum Monte Carlo (DQMC) simulations, we explore the emergence of various magnetic alignments as the ratio between the regular hopping amplitude, t, and the Rashba hopping term, t_R, is varied over a broad range of Hubbard interaction strengths, U. In the limit t_R→0, the system exhibits Néel antiferromagnetic order. However, when t~t_R, a spiral magnetic phase emerges due to the induced anisotropic Dzyaloshinskii–Moriya interaction. For t_R>t, we identify the onset of a spin vortex phase. At the extreme limit t=0(t_R≠0), we perform finite-size scaling analysis in the Weyl semimetal regime to pinpoint the quantum critical point associated with the spin vortex phase, employing sign-free Monte Carlo simulations. Additionally, we extract critical exponents consistent with a Gross-Neveu-type quantum phase transition.