Quasiparticle structure in the vicinity of the Heisenberg model in one and higher dimensions

We study quasiparticle structure in the vicinity of the Heisenberg model. At first, we focus on the model in one dimension and show how solitonic quasiparticles (and their bound states) emerge. Further we discuss its anlaog in higher dimensions. Related to this subject, numerical data are presented and a discussion is given for the quasiparticles in the two-dimensional Hubbard model at half filling on a triangular-type lattice.

Figure 1

Excitation spectrum at $J_1=-1$, $J_2=-0.3$, $\mathrm{\Delta }=0.6$, $L=12$,16,20,24.

Figure 2

Excitation spectrum at $J_1=-1;$ $J_2=-0.3$, $\mathrm{\Delta }=1$, $L=12$,16,20,24.

Figure 3

Excitation spectrum at $J_1=-1$, $J_2=-0.3$, $\mathrm{\Delta }=6$, $L=12$,16,20,24.

Figure 4

Excitation spectrum at $J_1=-1$, $J_2=-0.3$, $\mathrm{\Delta }=10$, $L=12$,16,20. The charge is ordered. The ground state is twofold degenerate in the thermodynamic limit.

Figure 5

$\mathbf{k}$-resolved charge compressibility $\kappa \left(\mathbf{k}\right)$ at $t^{\prime }∕t=0.5$, $U∕t=4$ for $\left[0,\pi \right)\times \left[0,\pi \right)$. In the absence of interaction $\left(U∕t=0\right)$, the $\kappa \left(\mathbf{k}\right)$ on $k_x+k_y=\pi$ is constant in this window. The result shows that finite interaction makes the system compressible around ($\pi ∕2$, $\pi ∕2$) more than $(k_x,k_y)=\left(\pi ,0\right),\left(0,\pi \right)$.