The one-dimensional XXZ model with long-range interactions

JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS

卷:226

Article; Proceedings Paper

Gonçalves, LL ; Vieira, AP ; Coutinho, LPS

关键词: quantum transitions;    one-dimensional systems;    long-range interactions;   

DOI  :  10.1016/S0304-8853(00)00690-9

来源: Elsevier

【 摘 要 】

The one-dimensional XXZ model (s = (1)/(2), N sites) with uniform long-range interactions among the transverse components of the spins is considered. The Hamiltonian of the model is explicitly given by H = J Sigma (N)(j=1) (s(j)(x)s(j+1)(x) + s(j)(y)s(j+1)(y)) - (I/N)Sigma (N)(j,k=1) s(j)(z)s(k)(z) - h Sigma (N)(j=1) s(j)(z), where the s(x,y,z) are half the Pauli spin matrices. The model is exactly solved by applying the Jordan-Wigner fermionization, followed by a Gaussian transformation. In the absence of the long-range interactions (I = 0), the model, which reduces to the isotropic XY model. is known to exhibit a second-order quantum-phase transition driven by the field at zero temperature. It is shown that in the presence of the long-range interactions (I not equal 0) the nature of the transition is strongly affected. For I > 0, which favours the ordering of the transverse components of the spins, the transition is changed from second to first order, due to the competition between transverse and xy couplings. On the other hand, for I < 0, which induces complete frustration of the spins, a second-order transition is still present, although the system is driven out of its usual universality class, and its critical exponents assume typical mean-field values. (C) 2001 Elsevier Science B.V. All rights reserved.

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