Persistent Currents in the Heisenberg chain with a weak link
T.M.R. Byrnes, R.J. Bursill, H.-P. Eckle, C.J. Hamer, and A. W., Sandvik
TL;DR
This paper investigates how a weak link affects persistent currents in a Heisenberg spin chain, using numerical methods to confirm theoretical predictions that the currents diminish as the link weakens.
Contribution
It provides numerical evidence supporting the renormalization group predictions that persistent currents vanish in the presence of a weak link in the Heisenberg chain.
Findings
Spin/charge stiffness scales to zero with a weak link
Results agree with renormalization group predictions
Persistent currents are suppressed by the weak link
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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