Near-Boundary and Bulk Regions of a Semi-Infinite Two-Dimensional Heisenberg Antiferromagnet

Using the spin-wave approximation elementary excitations of a semi-infinite two-dimensional $S=\frac{1}{2}$ Heisenberg antiferromagnet are considered. The spectrum consists of bulk modes – standing spin waves and a quasi-one-dimensional mode of boundary spin waves. These latter excitations eject bulk modes from two boundary rows of sites, thereby dividing the antiferromagnet into two regions with different dominant excitations. As a result absolute values of nearest-neighbor spin correlations on the edge exceed the bulk value.