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Physica A Statistical Mechanics and its Applications

Quantum Monte-Carlo study of the Heisenberg chain with long-range ferromagnetic interactions

Oleg N. Vassiliev, I. V. Rojdestvenski, Michael G Cottam

Published May 1, 2001• 9 citations
Publisher
DOI
10.1016/s0378-4371(01)00125-x

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Within a random phase approximation,the quantum Heisenberg ferromagnetic chain with long-range interaction proportional to r-p was studied by Green-function method.The results indicated that for exchange interaction decaying as r-p for 1p2,there existed a phase transition at finite temperature,and that no transition to a ferromagnetic phase at any finite temperature occurs for p≥2.The results are reasonable agreement with those of the Monte Carlo calculations and the other theoretical approaches.
We study an open Heisenberg XXZ spin chain with long-range Ising-type interaction, which is incoherently driven at its boundaries and, therefore, a far-from-equilibrium steady-state current is induced. Quantum Monte Carlo techniques make a regime accessible where the system size is large enough to examine the transition from a diffusive to a ballistic transport regime. We find that the chain lengths for this transition are increasing with decreasing range of the Ising-type interactions between distant spins, whereas the strength of the incoherent driving does not have a relevant effect on the transport transition. The transition can be explained by the suppression of ferromagnetic domains at the edges of the chain.