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The one-dimensional XXZ model with long-range interactions | | L. L. Goncalves
; A. P. Vieira
; L. P. S. Coutinho
; | | Date: |
16 Aug 2000 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | U. do Ceara), A. P. Vieira (U. de Sao Paulo), L. P. S. Coutinho (U. do Ceara | | Abstract: | 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 $H=Jsum_{j=1}^{N}(s_{j}^{x}s_{j+1}^{x}+s_{j}^{y}s_{j+1}^{y}) -(I/N)sum_{j,k=1}^{N}s_{j}^{z}s_{k}^{z}-hsum_{j=1}^{N}s_{j}^{z},$ 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 different from 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. | | Source: | arXiv, cond-mat/0008230 | | Services: | Forum | Review | PDF | Favorites | |
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