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Journal of Physics Condensed Matter

Spin excitations in the S=1/2 Heisenberg antiferromagnetic model on a square lattice

А. Ф. Барабанов, Leonid A. Maksimov, Oleg A. Starykh, G. Uimin

Published Nov 12, 1990• 2 citations
Publisher

Abstract

The authors investigate the properties of the two-dimensional quantum S=1/2 Heisenberg antiferromagnetic model on a square lattice by means of a block approach. The lattice is divided into four spin square blocks and the Hamiltonian is expressed in terms of low-energy block states. In the framework of the mean-field theory based on the 'auxiliary-boson' formalism; they show that the spin excitation spectrum contains one singlet mode with the temperature-dependent gap and three degenerate triplet modes. The asymptotic low-temperature spin-spin correlations are proportional to R -3/2 exp(-R(1/ xi 1 +1/ xi 2 )), where xi 1 =exp(A/T), xi 2 =constant and A approximately=0.5J. The uniform susceptibility tends to zero in agreement with numerical results; the energy per site is close to -0.57J. Beyond the meanfield theory the authors find gapless collective excitations analogous to the gapless mode in the neutral Fermi gas with attraction.

DOI
10.1088/0953-8984/2/45/006

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The authors investigate the properties of the two-dimensional quantum S=1/2 Heisenberg antiferromagnetic model on a square lattice by means of a block approach. The lattice is divided into four spin square blocks and the Hamiltonian is expressed in terms of low-energy block states. In the framework of the mean-field theory based on the 'auxiliary-boson' formalism; they show that the spin excitation spectrum contains one singlet mode with the temperature-dependent gap and three degenerate triplet modes. The asymptotic low-temperature spin-spin correlations are proportional to R -3/2 exp(-R(1/ xi 1 +1/ xi 2 )), where xi 1 =exp(A/T), xi 2 =constant and A approximately=0.5J. The uniform susceptibility tends to zero in agreement with numerical results; the energy per site is close to -0.57J. Beyond the meanfield theory the authors find gapless collective excitations analogous to the gapless mode in the neutral Fermi gas with attraction.
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Spin excitation spectra of two dimensional S=1/2S=1/2S=1/2 Heisenberg model with checkerboard structures.
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The exact excitation spectrum of a 3×3 two dimensional square lattice interacting via the nearest neighbour anisotropic Heisenberg Hamiltonian H = J ∑ < i j > { S i z S j z +γ( S i x S j x + S i y S j y )}, has been obtained for various values of the anisotropy constant γ. The zeros of the partition function in the complex µ=exp (- m H e / k B T ) plane are calculated for different γ for both ferromagnetic ( J <0) and antiferromagnetic ( J >0) coupling. For 0⩽γ⩽10{\leqslant}\gamma{\leqslant}10⩽γ⩽1, the ferromagnetic zeros obey the generalized Lee-Yang theorem at all temperatures, but, for γ>1, they violate it at sufficiently low temperatures. For antiferromagnetic coupling, the zeros lie on the (unphysical) negative real axis for all values of γ and temperature. The zero-field susceptibility, for antiferromagnetic coupling, does not display a local maximum as a function of temperature in contrast to Kawabata's results on the same lattice.
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Using a modified Lanczos method we have studied the two-dimensional Heisenberg antiferromagnetic model (at zero temperature) with lattices up to 24 sites. The ground-state and first-excited-state energies are evaluated. We show that the model is gapless in the thermodynamic limit in agreement with recent Monte Carlo simulations. Accurate results for the ``square ladder'' are also presented showing that this model is massive. The finite-size dependence of the results is discussed. In addition, we calculate the energy of a resonating-valence-bond state on finite lattices and its overlap with the exact ground state.
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