Dynamical domain walls and spin-Peierls order in doped antiferromagnets: Evidence from exact diagonalization of small clusters

Abstract

The hole-doped two-dimensional(2D) $t\ensuremath{-}J$ model is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster which, unlike the standard tilted-square clusters, can in principle accomodate an antiphase domain wall. For hole concentration $10%$ and $J/t>~0.5$ the ground-state energy/site is lower than the conventional tilted-square $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ cluster. In the ground state two holes form a loosely bound pair pinned to an antiphase domain wall. The dynamical density correlation function shows sharp quasiparticlelike peaks, reminiscent of the ``holons'' in 1D chains, which suggest the existence of solitonlike propagating domain walls. The dynamical correlation function of the bond-singlet operator has a low-energy peak structure characteristic of columnar spin-Peierls order, the dynamical spin-correlation function shows an intense and isolated ``resonance peak'' near $(\ensuremath{\pi},\ensuremath{\pi}).$