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

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

2009-01-07

arxiv.org/abs/0901.0894v2

Phys. Rev. B 79, 094413 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 7 figures added references

Scientific paper

10.1103/PhysRevB.79.094413

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.

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