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Physica A Statistical Mechanics and its Applications

A thermodynamic approximation of the ground state of antiferromagnetic heisenberg spin− lattices

G.I. Tielen, Paul Louis Iske, W.J. Caspers

Published May 1, 1991• 3 citations
Publisher
DOI
10.1016/0378-4371(91)90376-n

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We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpinski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpinski gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin-spin correlations and specific heat data and conclude that the s=1/2 quantum antiferromagnet on the Sierpinski gasket shows a disordered magnetic ground state with on the Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of xiapproximate to1 and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.

•Jan 1, 2004•2 citations
The Heisenberg antiferromagnet on the maple-leaf lattice has recently gathered a great deal of attention. Competition between three nonequivalent bond interactions results in various ground-state quantum phases, with the exact dimer-product singlet ground state being among them. The thermodynamic properties of this model are much less understood. We used high-temperature expansion up to the 18th order to study the thermodynamics of the S = 1 / 2 Heisenberg model on the uniform maple-leaf lattice with the ground state exhibiting a six-sublattice 120 ∘ long-range magnetic order. Padé approximants allow us to get reliable results up to the temperatures of about T ≈ 0.4 . To study thermodynamics for arbitrary temperatures, we made the interpolation using the entropy method. Based on the analysis of close Padé approximants, we find ground-state energy e 0 = − 0.53064 ... − 0.53023 in good agreement with numerical results. The specific heat c ( T ) has a typical maximum at rather low temperatures T ≈ 0.379 and the uniform susceptibility χ ( T ) at T ≈ 0.49 . We also estimate the value of χ ( T ) at zero temperature χ 0 ≈ 0.05 ... 0.06 . The ground-state order manifests itself in the divergence of the so-called generalized Wilson ratio.
By utilizing tensor-network-based methods, we investigate the zero- and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnetic (HAF) model on an infinite Husimi lattice that contains 3/2 sites per triangle. The ground state of this model is found to possess vanishing local magnetization and is featureless; the spin-spin and dimer-dimer correlation functions are verified to decay exponentially, and its ground-state energy per site is determined to be ${e}_{0}=\ensuremath{-}0.4343(1)$, which is very close to that [${e}_{0}=\ensuremath{-}0.4386(5)$] of the intriguing kagome HAF model. The magnetization curve shows the absence of a zero-magnetization plateau, implying a gapless excitation. A 1/31/31/3-magnetization plateau with spin-up-up-down state is observed, which is selected and stabilized by quantum fluctuations. A ground-state phase diagram under magnetic fields is presented. Moreover, both magnetic susceptibility and the specific heat are studied, whose low-temperature behaviors reinforce the conclusion that the HAF model on the infinite Husimi lattice owns a gapless and featureless spin-liquid ground state.
We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpinski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpinski gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin-spin correlations and specific heat data and conclude that the s=1/2 quantum antiferromagnet on the Sierpinski gasket shows a disordered magnetic ground state with on the Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of xiapproximate to1 and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.