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 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 Néel 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.

arXiv comment4 pages, 7 figures added references

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Cited by in corpus (12)

• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• Genuine Multipartite Entanglement Trends in Gapless-gapped Transitions of Quantum Spin Systems
• Magnetic order on a frustrated spin-1/2 Heisenberg antiferromagnet on the Union Jack lattice
• Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure
• A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$
• Entanglement in first excited states of some many-body quantum spin systems: indication of quantum phase transition in finite size systems
• Spin correlations near the surface of a three-dimensional Heisenberg antiferromagnet
• Near-Boundary and Bulk Regions of a Semi-Infinite Two-Dimensional Heisenberg Antiferromagnet
• Excitations and spin correlations near the interface of two three-dimensional Heisenberg antiferromagnets
• The t-J model on a semi-infinite lattice