Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain

Details Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain

2011-07-14

arxiv.org/abs/1107.2907v2

Physics

Condensed Matter

Strongly Correlated Electrons

24 pages, 25 figures, typos corrected, one figure added and minor revisions of text performed

Scientific paper

The contribution to the entanglement of an impurity attached to one end of a $J-J_2-delta$ quantum spin chain (S=1/2) is studied. Two different measures of the impurity contribution to the entanglement have been proposed: the impurity-entanglement-entropy S_{imp} and the negativity N. The first, S_{imp}, is based on a subtractive procedure where the entanglement-entropy in the absence of the impurity is subtracted from results with the impurity present. The other, N, is the negativity of a part of the system separated from the impurity and the impurity itself. In this paper we compare the two measures and discuss similarities and differences between them. In the $J-J_2-\delta$ model it is possible to perform very precise variational calculations close to the Majumdar-Ghosh-point (J_2 = J / 2 and \delta = 0) where the system is gapped with a two-fold degenerate dimerized ground-state. We describe in detail how such calculations are done and how they can be used to calculate N as well as S_{imp} for any impurity-coupling J_K. We then study the complete cross-over in the impurity entanglement as J_K is varied between 0 and 1 close to the Majumdar-Ghosh-point. In particular we study the impurity entanglement when a staggered nearest-neighbour-interaction proportional to $\delta$ is introduced. In this case, the two-fold degeneracy of the ground-state is lifted leading to a very rapid reduction in the impurity entanglement as $\delta$ is increased.

Affiliated with

Also associated with

No associations

Rating

Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Impurity Entanglement in the $J-J_2-δ$ Quantum Spin Chain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226145