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

TL;DR

This paper investigates how boundary-induced Dimer correlations in square-lattice Heisenberg models vary with different interactions, revealing that Dimer correlations near edges are short-ranged deep inside the Ne9el phase, impacting the nature of phase transitions.

Contribution

It provides a detailed analysis of boundary-induced Dimer correlations in frustrated and anisotropic square-lattice Heisenberg models, highlighting their behavior and implications for phase transitions.

Findings

Dimer correlations become longer ranged as anisotropy decreases.

Increased frustration strengthens but shortens Dimer correlations near the boundary.

Deep inside the Ne9el phase, Dimer correlations remain short-ranged.

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 non-linear 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 $J_1-J_2$ model with nearest and second neighbor couplings and (ii) a spatially anisotropic Heisenberg model, with nearest-neighbor couplings $J$ perpendicular to the boundary and $J^\prime$ parallel to the boundary. We find that in the latter model, as $J^\prime/J$ 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\'{e}el phase of the $J_1-J_2$ 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.