Figure 1

(Color online) Charge and spin configurations of a $t\text{−}J$ model in a pinned checkerboard configuration. The results show the expectation value of $⟨S_z⟩$ and $⟨n_h⟩$ for a $10\times 8$ $t\text{−}J$ cluster with cylindrical boundary conditions: open in $x$, periodic in $y$. Here there are eight holes and $J∕t=0.35$. Initially, a local pinning potential of $-0.5t$ was placed on the 16 sites making up four the plaquettes visible in the left panel. Nine sweeps were performed, keeping up to $m=1000$ states, with the result shown in the left panel. Subsequently, the pinning potential was turned off. In the right panel, we show the result after three more sweeps were performed, reaching $m=1500$ states.Reuse & Permissions

Figure 2

(Color online) Charge and spin configurations of a $t\text{−}J$ cluster with two sites pinned with a local potential of $-0.5t$. In each panel, the sites pinned have the large circles. The lower plot shows the total energies of the systems as a function of the number of states kept per block as DMRG sweeps were performed on the systems.Reuse & Permissions

Figure 3

(Color online) Charge and spin configurations with different values of the exchange coupling linking vertical and horizontal bonds. In both cases $J_x=0.35$. In the left panel, $J_y=0.37$, and in the right, $J_y=0.38$.Reuse & Permissions

Figure 4

(Color online) Charge and spin configurations with a local field in a pattern transverse to the stripes applied. In the simulation shown in the left (right) panel, potentials of $-0.05t$ $(-0.1t)$ were applied to four of the horizontal rows of sites: rows 2, 3, 6, and 7.Reuse & Permissions

Figure 5

Charge-density-wave response to an applied local potential on a two-leg $t\text{−}J$ ladder, with doping 0.25. The applied field had periodicity 4 with rungs 1 and 2 with $+ϵ$, rows 3 and 4 with $-ϵ$, etc. The measured response $\Delta n$ is the absolute difference in hole densities between sites $2n$ and $2n+1$.Reuse & Permissions