Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2007-03-02
J. Stat. Mech. (2007) P08003
Physics
Condensed Matter
Strongly Correlated Electrons
62 pages, 27 figures, JSTAT macros
Scientific paper
10.1088/1742-5468/2007/08/P08003
Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S=-Tr rho_A log rho_A, for a sub-system A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, S_{imp}, is defined and analyzed in detail in both the gapless, J_2 <= J_2^c, as well as the dimerized phase, J_2>J_2^c, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J_2 <= J_2^c, gives rise to a large length scale, xi_K, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form S_{imp}(r/xi_K,r/R) for a system of size R. Numerical results are presented clearly demonstrating this scaling. At the critical point, J_2^c, an analytic Fermi liquid picture is developed and analytic results are obtained both at T=0 and T>0. In the dimerized phase an appealing picure of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar-Ghosh point, J_2=J_1/2, and surprisingly precise even close to the critical point J_2^c. In appendices the relation between the finite temperature entanglement entropy, S(T), and the thermal entropy, S_{th}(T), is discussed and and
Affleck Ian
Chang Ming-Shyang
Laflorencie Nicolas
Sørensen Erik S.
No associations
LandOfFree
Quantum Impurity Entanglement 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 Quantum Impurity Entanglement, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Impurity Entanglement will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-284252