Naslov
Renyi entropy of the XY spin chain

Autori
Franchini, F ; Its, A R ; Korepin, V E

Izvornik
Journal of Physics A: Mathematical and Theoretical (1751-8113) 41 (2007), 2; 025302-18

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, ostalo

Ključne riječi
Entanglement, Renyi Entropy, XY Chain

Sažetak
We consider the one-dimensional XY quantum spin chain in a transverse magnetic field. We are interested in the Renyi entropy of a block of L neighboring spins at zero temperature on an infinite lattice. The Renyi entropy is essentially the trace of some power α of the density matrix of the block. We calculate the asymptotic for L→∞ analytically in terms of Klein's elliptic λ - function. We study the limiting entropy as a function of its parameter α. We show that up to the trivial addition terms and multiplicative factors, and after a proper re-scaling, the Renyi entropy is an automorphic function with respect to a certain subgroup of the modular group ; moreover, the subgroup depends on whether the magnetic field is above or below its critical value. Using this fact, we derive the transformation properties of the Renyi entropy under the map α→α−1 and show that the entropy becomes an elementary function of the magnetic field and the anisotropy when α is a integer power of 2, this includes the purity trρ2. We also analyze the behavior of the entropy as α→0 and ∞ and at the critical magnetic field and in the isotropic limit [XX model].

Izvorni jezik
Engleski

POVEZANOST RADA