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Persistent Currents in the Heisenberg chain with a weak link

T. M. R. Byrnes·R. J. Bursill·H. -P. Eckle·C. J. Hamer·A. W. Sandvik
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Abstract

The Heisenberg chain with a weak link is studied, as a simple example of a quantum ring with a constriction or defect. The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the `persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.

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T. M. R. Byrnes, R. J. Bursill, H. -P. Eckle, C. J. Hamer, A. W. Sandvik. 2002-05-14. Persistent Currents in the Heisenberg chain with a weak link. https://doi.org/10.1103/physrevb.66.195313

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