# Table 6 Phase parameters required to simulate the time evolution of the vertical hopping $$h_{5}$$, see Eq. (108e)

Vertical Hopping

Operator

$$\tilde{\varphi }_{1}$$

$$\tilde{\varphi }_{2}$$

$$U_{(6,8)}^{{y,y}^{\dagger }}$$

$$\tilde{\varphi }^{5,8}_{1}= \pi$$

$$\tilde{\varphi }^{5,8}_{2}=\pi$$

$$U_{7}^{x}$$

$$\tilde{\varphi }^{7}_{1}= 2\pi$$

$$\tilde{\varphi }^{7}_{2}=\pi$$

$$\operatorname{exp} (-\frac{i\mathcal{A}}{2}\sigma _{6}^{x}\sigma _{7}^{y}\frac{t}{n} )$$

$$\tilde{\varphi }^{6}_{1}= 1/2\pi$$

$$\tilde{\varphi }^{6}_{2}=3/2\pi$$

$$U_{7}^{x^{\dagger }}$$

$$\tilde{\varphi }^{7}_{1}= \pi$$

$$\tilde{\varphi }^{7}_{2}={2}\pi$$

$$U_{(6,8)}^{y,y}$$

$$\tilde{\varphi }^{5,8}_{1}={2} \pi$$

$$\tilde{\varphi }^{5,8}_{2}={2}\pi$$

$$U_{(6,8)}^{{x,x}^{\dagger }}$$

$$\tilde{\varphi }^{5,8}_{1}=\pi$$

$$\tilde{\varphi }^{5,8}_{2}=2\pi$$

$$U_{7}^{y^{\dagger }}$$

$$\tilde{\varphi }^{7}_{1}=\pi$$

$$\tilde{\varphi }^{7}_{2}=\pi$$

$$\operatorname{exp} (-\frac{i\mathcal{A}}{2}\sigma _{6}^{y}\sigma _{7}^{x}\frac{t}{n} )$$

$$\tilde{\varphi }^{6}_{1}=3/2\pi$$

$$\tilde{\varphi }^{6}_{2}=3/2\pi$$

$$U_{7}^{y}$$

$$\tilde{\varphi }^{7}_{1}=2\pi$$

$$\tilde{\varphi }^{7}_{2}=2\pi$$

$$U_{(6,8)}^{x,x}$$

$$\tilde{\varphi }^{5,8}_{1}=2\pi$$

$$\tilde{\varphi }^{5,8}_{2}=\pi$$