A numerical analysis of a one-dimensional Hamiltonian system, composed by N classical localized Heisenberg rotators on a ring, is presented. A distance r ij between rotators at sites i and j is introduced, such that the corresponding two-body interaction decays with r ij as a power-law, 1/r α ij (α ≥ 0). The index α controls the range of the interactions, in such a way that one recovers both the fully-coupled (i.e., mean-field limit) and nearest-neighbour-interaction models in the particular limits α = 0 and α → ∞, respectively. The dynamics of the model is investigated for energies U below its critical value (U < U c ), with initial conditions corresponding to zero magnetization. The presence of quasi-stationary states (QSSs), whose durations t QSS increase for increasing values of N , is verified for values of α in the range 0 ≤ α < 1, like the ones found for the similar model of XY rotators. Moreover, for a given energy U , our numerical analysis indicates that t QSS ∼ N γ , where the exponent γ decreases for increasing α in the range 0 ≤ α < 1, and particularly, our results suggest that γ → 0 as α → 1. The growth of t QSS with N could be interpreted as a breakdown of ergodicity, which is shown herein to occur for any value of α in this interval.
We study spin transport in one-and two-dimensional Heisenberg antiferromagnets. In one dimension we take spin S = 1. The longitudinal spin conductivity is calculated using the Kubo formula. The magnetic properties of low-dimensional systems are significantly modified by strong correlations effects. The models studied here show unconventional transport behavior: the computed spin conductivity exhibits a nonzero Drude weight at finite temperatures and thus a ballistic character. We present results for the regular part of the conductivity as a function of the frequency.
In this paper we present a study of the phase diagram and critical properties of the square-lattice quantum XY model, with a single-ion anisotropy and spin S = 1, as a function of the anisotropy parameter D. For D less than a critical value D C , which is the critical point for a quantum phase transition at T = 0, the model presents a Berezinskii-Kosterlitz-Thouless (BKT) transition. This region is adequately described by the self-consistent harmonic approximation. We show that, if we want to use a Schwinger boson theory in this region, we should include fluctuations around the mean-field approximation (which leads to a gauge field) to describe correctly the BKT transition. However both methods are inadequate to describe the large-D phase, and we show that this phase can be studied using the bond operator formalism which gives the correct behaviour for the correlation length as a function of the temperature in the critical point and above. Our results agree with scaling arguments.
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