Energetics of Domain Walls in the 2D t − J Model

Abstract

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