Spin correlations near the edge as probe of dimer order in square-lattice Heisenberg models

Abstract

Recent numerical and analytical work has shown that for the square-lattice Heisenberg model the boundary can induce dimer correlations near the edge which are absent in spin-wave theories and nonlinear sigma model approaches. Here, we calculate the nearest-neighbor spin correlations parallel and perpendicular to the boundary in a semi-infinite system for two different square-lattice Heisenberg models: (i) a frustrated ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with nearest- and second-neighbor couplings and (ii) a spatially anisotropic Heisenberg model, with nearest-neighbor couplings $J$ perpendicular to the boundary and ${J}^{\ensuremath{'}}$ parallel to the boundary. We find that in the latter model, as ${J}^{\ensuremath{'}}/J$ is reduced from unity, the dimer correlations near the edge become longer ranged. In contrast, in the frustrated model, with increasing ${J}_{2}$, dimer correlations are strengthened near the boundary but they decrease rapidly with distance. These results imply that deep inside the N\'eel phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, dimer correlations remain short ranged. Hence, if there is a direct transition between the two, it is either first order or there is a very narrow critical region.