Subtlety of Determining the Critical Exponent $\nu$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice

Abstract

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent $\nu$ are analyzed in great detail. Remarkly, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent $\nu =0.691(2)$ with that calculated in \cite{Wenzel08}. However by using the data with large number of spins $N$, we obtain $\nu =0.707(6)$ which agrees with the most accurate Monte Carlo O(3) value $\nu =0.7112(5)$ as well.

7 pages, 9 figures, 1 table, version accepted for publishing

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• Quantum Phase Transition, O(3) Universality Class and Phase Diagram of Spin-1/2 Heisenberg Antiferromagnet on Distorted Honeycomb Lattice: A Tensor Renormalization Group Study
• Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model
• Ferromagnetically coupled dimers on the distorted Shastry-Sutherland lattice: Application to (CuCl)LaNb2O7
• Quantum phase transition, universality and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on honeycomb lattice
• Quantum Monte Carlo Study on the Spin-1/2 Honeycomb Heisenberg Model with Mixing Antiferromagnetic and Ferromagnetic Interactions in External Magnetic Fields
• Entanglement and quantum correlations in the XX spin-$1/2$ honeycomb lattice
• Universal scalings of Néel temperature, staggered magnetization density, and spinwave velocity of three-dimensional disordered and clean quantum antiferromagnets
• Anomalous scaling corrections and quantum phase diagram of the Heisenberg antiferromagnet on the spatially anisotropic honeycomb lattice
• Entanglement entropy for the valence bond solid phases of two-dimensional dimerized Heisenberg antiferromagnets
• Exact staggered dimer ground state and its stability in a two-dimensional magnet