Weyl semimetallic, N\'eel, spiral, and vortex states in the Rashba-Hubbard model

TL;DR

This paper explores how magnetic phases in the Rashba-Hubbard model on a square lattice evolve with varying Rashba spin-orbit coupling and interaction strength, revealing transitions from antiferromagnetic to vortex states.

Contribution

It provides a comprehensive analysis of magnetic phase transitions in the Rashba-Hubbard model using advanced numerical methods, identifying new vortex and spiral magnetic phases.

Findings

Néel antiferromagnetic order at low Rashba coupling

Emergence of spiral magnetic phase at comparable hopping amplitudes

Onset of spin vortex phase at high Rashba coupling

Abstract

We investigate the evolution of magnetic phases in the Hubbard model under strong Rashba spin-orbit coupling on a square lattice. By using Lanczos exact diagonalization and 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 $t_R \rightarrow 0$, the system exhibits N\'eel antiferromagnetic order, while when $t \sim t_R$, 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 \neq 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 quantum Monte Carlo simulations - the extracted critical exponents are consistent with a Gross-Neveu-type quantum phase transition.