Driven isotropic Heisenberg spin chain with arbitrary boundary twisting angle: exact results
arXiv:1310.1315 · doi:10.1103/PhysRevE.88.062118
Abstract
We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady steady state of a chain with N sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle θ. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady state currents scale as 1/N^2 for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to 2θ/N.
12 pages, 5 figures close to published version; misprints corrected, one Figure revised
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Cited by in corpus (42)
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