Energetics of Domain Walls in the 2D $\mathit{t}-\mathit{J}$ Model

Using the density matrix renormalization group, we calculate the energy of a domain wall in the 2D $t-J$ model as a function of the linear hole density ${\rho }_{\ell }$, as well as the interaction energy between walls, for $J/t=0.35\mathrm{}$. Based on these results, we conclude that the ground state always has domain walls for dopings $0<x\lesssim 0.3$. For $x\lesssim 0.125$, the system has (1, 0) domain walls with ${\rho }_{\ell }\sim 0.5$, while for $0.125\lesssim x\lesssim 0.17$ the system has a possibly phase-separated mixture of walls with ${\rho }_{\ell }\sim 0.5$ and ${\rho }_{\ell }=1\mathrm{}$. For $x\gtrsim 0.17$, there are only walls with ${\rho }_{\ell }=1\mathrm{}$.