Figure 1

(Color online) (a) Support of the single-particle spectral function. $A\left(\omega ,P\right)$ is nonvanishing in the shaded areas. ${ϵ}_s\left(P\right)$ is the dispersion relation of the collective spin excitations (“spinons”). The blue lines depict the linearized dispersions $\pm v_s\left(P-k_F\right)$ and $\pm v_s\left(P+k_F\right)$ that underlie the Luttinger liquid approximation. (b) Structure of the single-particle spectral function in the Luttinger liquid approximation for momenta close to $k_F$ and $P<k_F$. There is a singularity at negative frequencies $\omega =-v_s\left(k_F-P\right)$ and a power-law “shoulder” at positive frequencies $\omega =v_c\left(k_F-P\right)$.Reuse & Permissions

Figure 2

Power-law singularity in the single-hole spectral function for $\left|P\right|<k_F$. There is a singularity at negative frequencies $\omega ={ϵ}_s\left(P\right)$ with a momentum-dependent exponent ${\mu }_{0,-}$ and a power-law “shoulder” at positive frequencies $\omega =-{ϵ}_s\left(P\right)$.Reuse & Permissions

Figure 3

Distribution of integers for the holon-spinon excitation for $N_{\text{GS}}=14$, $M_{\text{GS}}=7$. The positions of the two holes are $I^h$ and ${\Lambda }^h$ respectively. We have shown the configuration where the $I_j$ range from $\frac{N_{\text{GS}}}{2}-1$ to $\frac{N_{\text{GS}}}{2}$, but we equally well can choose them $\frac{N_{\text{GS}}}{2}\le I_j\le \frac{N_{\text{GS}}}{2}-1$. The two possibilities give rise to the two signs in Eq. (27).Reuse & Permissions

Figure 4

Boundaries of the holon-spinon excitation continuum in zero magnetic field for (a) $u=1$ and density $n_c=0.5$ and (b) for $u=1$ and $n_c=0.2$.Reuse & Permissions

Figure 5

(Color online) Boundaries of the holon–3 spinon excitation continuum in zero magnetic field for (a) $u=1$ and density $n_c=0.5$ and (b) for $u=1$ and $n_c=0.2$. The boundaries of the holon-spinon continua are depicted by the dashed blue lines.Reuse & Permissions

Figure 6

(Color online) $N_c^{\text{imp}}$ as a function of momentum for $u=0.5,1,2$ and densities (a) $n_c=0.2$ and (b) $n_c=0.5$.Reuse & Permissions

Figure 7

(Color online) $D_c^{\text{imp}}$ as a function of momentum for $u=0.5,1,2$ and densities (a) $n_c=0.2$ and (b) $n_c=0.5$.Reuse & Permissions

Figure 8

Distribution of integers for the threshold of the holon–3 spinon excitation. The hole in the distribution of $I_j$ is at $-\left(N_{\text{GS}}-1\right)/2$ and the three holes in the distribution of $J_{\alpha }$ occur at $\pm M_{\text{GS}}/2$ and $J^h$, respectively.Reuse & Permissions

Figure 9

(Color online) Threshold singularity exponent ${\mu }_{0,-}$ as a function of momentum for $n_c=0.6$.Reuse & Permissions