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The European Physical Journal B

High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

Fu-Jiun Jiang

Published Dec 1, 2012• 10 citations
Publisher
DOI
10.1140/epjb/e2012-30784-7

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The magnetic properties of the two-dimensional S = 1 2 (quantum) antiferromagnetic Heisenberg model on a honeycomb lattice with and without interlayer coupling are studied by means of a continuous Euclidean time Quantum-Monte-Carlo algorithm.The internal energy, the magnetic susceptibility and the staggered magnetization are determined in the full temperature range.For the two-dimensional system the groundstate energy/bond is found to be E hc 0 = -0.36303(13),and the zero temperature staggered magnetization m st = 0.2681(8).For coupled planes of honeycomb systems a phase transition from an ordered phase to a disordered phase is found at T /J = 0.695(10).
We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size periodic lattices.
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.