Monte Carlo study of the two-dimensional spin-1/2 XY model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto a three-dimensional Ising model with complicated many-spin interactions. This relationship is used to construct an efficient Monte Carlo algorithm. Simulation data for the specific heat and vortex correlation functions give strong evidence for the existence of a phase transition.     

Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet

We report a neutron scattering study of the instantaneous spin correlations in the two-dimensional spin S =5/2 square-lattice Heisenberg antiferromagnet Rb₂MnF₄. The measured correlation lengths are quantitatively described, with no adjustable parameters, by high-temperature series expansion results and by a theory based on the quantum self-consistent harmonic approximation. Conversely, we find that the data, which cover the range from about 1 to 50 lattice constants, are outside of the regime corresponding to renormalized classical behavior of the quantum non-linear model. In addition, we observe a crossover from Heisenberg to Ising critical behavior near the Néel temperature; this crossover is well described by a mean-field model with no adjustable parameters. Received: 3 March 1998 / Received in final form: 4 May 1998 / Accepted: 19 May 1998     

Calculation of correlation functions in the Heisenberg spin-1/2 antiferromagnetic model

We derive the exact expression of the four-spinon contribution S ₄ to the dynamical correlation function S of the spin 1/2 isotropic (XXX) He isenberg model in the antiferromagnetic regime using the quantum group symmetry of the model. We first give the exact expression for the n-spinon contribution in the form of contour integrals and display known results regarding the two-spinon contribution S ₂. Then we specialize the n-spinon formula to the case n = 4 and compute three sum rules for S ₄ that the total S is known to satisfy exactly. These are: the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that S ₄ corrects only by a small amount the contribution from S ₂. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

The low-energy constants, namely the spin stiffness ρ _s , the staggered magnetization density ? _s per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J ₁ and J ₂ in the spatial 1- and 2-directions, respectively. For each considered J ₂∕J ₁, the aspect ratio of the corresponding linear box sizes L ₂∕L ₁ used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρ _s1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J ₂∕J ₁. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ? _s and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.     

The spin-1/2 antiferromagnetic Heisenberg chain with competing interactions

We investigate the thermodynamical and magnetic properties of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with competing interactions near the transition between the "dimer phase" and the "frustrated phase".     

System-size effect versus staggered magnetization in the antiferromagnetic Heisenberg XXZ chains: A Monte Carlo study

Monte Carlo simulations of the antiferromagnetic Heisenberg XXZ chains are carried out on a larger system than in a previous paper. System-size effect versus staggered magnetization is severe in the vicinity of the anisotropy parameter Δ = 1.0. The result obtained for spin-1 supports Haldane's conjecture that a gap exists in the excitation spectrum in the vicinity of Δ = 1.0.     

Monte Carlo study of half-magnetization plateau and magnetic phase diagram in pyrochlore antiferromagnetic Heisenberg model

The antiferromagnetic Heisenberg model on a pyrochlore lattice under external magnetic field is studied by classical Monte Carlo simulation. The model includes bilinear and biquadratic interactions; the latter effectively describes the coupling to lattice distortions. The magnetization process shows a half-magnetization plateau at low temperatures, accompanied with strong suppression of the magnetic susceptibility. Temperature dependence of the plateau behavior is clarified. Finite-temperature phase diagram under the magnetic field is determined. The results are compared with recent experimental results in chromium spinel oxides.     

Bipartite entanglement in spin-1/2 Heisenberg model

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ－1, and it may keep a steady value of 0.5 in the region of B2－γ²]^1/2 if Δ>γ－1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δ_c (Δ_c=γ－1 and (γ²－1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.