# Exotic Spin Phases in Two Dimensional Spin-orbit Coupled Models: Importance of Quantum Fluctuation Effects

## TL;DR

This paper explores how quantum fluctuations influence exotic spin phases in two-dimensional spin-orbit coupled models derived from Fermi-Hubbard and Bose-Hubbard systems, revealing stabilization of spiral and skyrmion phases.

## Contribution

It demonstrates the significant role of quantum fluctuations in stabilizing exotic spin phases, including spiral and skyrmion phases, in models with Rashba spin-orbit coupling.

## Key findings

- Quantum fluctuations stabilize spiral and skyrmion phases.
- Quantum order-by-disorder reduces classical in-plane phases.
- Quantum fluctuation energies are significant across the entire Fermi-Hubbard regime.

## Abstract

We investigate the phase diagrams of the effective spin models derived from Fermi-Hubbard and Bose-Hubbard models with Rashba spin-orbit coupling, using string bond states, one of the quantum tensor network states methods. We focus on the role of quantum fluctuation effect in stabilizing the exotic spin phases in these models. For boson systems, and when the ratio between inter-particle and intra-particle interaction $\lambda > 1$, the out-of-plane ferromagnetic (FM) and antiferromagnetic (AFM) phases obtained from quantum simulations are the same to those obtained from classic model. However, the quantum order-by-disorder effect reduces the classical in-plane XY-FM and XY-vortex phases to the quantum X/Y-FM and X/Y-stripe phase when $\lambda < 1$. The spiral phase and skyrmion phase can be realized in the presence of quantum fluctuation. For the Fermi-Hubbard model, the quantum fluctuation energies are always important in the whole parameter regime. %, which are much larger than those of the Bose model. A general picture to understand the phase diagrams from symmetry point of view is also presented.