Entanglement entropy of aperiodic quantum spin chains

¹  Research Institute for Solid State Physics and Optics - H-1525 Budapest, P.O. Box 49, Hungary
²  Institute of Theoretical Physics, Szeged University - H-6720 Szeged, Hungary
³  Research Institute for Particle and Nuclear Physics - H-1525 Budapest, P.O. Box 49, Hungary

Received: 3 April 2007
Accepted: 18 June 2007

Abstract

We study the entanglement entropy of blocks of contiguous spins in non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg, XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and relevant aperiodic modulations, the entanglement entropy is found to be a logarithmic function of the block size with log-periodic oscillations. The effective central charge, , defined through the constant in front of the logarithm may depend on the ratio of couplings and can even exceed the corresponding value in the homogeneous system. In the strong modulation limit, the ground state is constructed by a renormalization group method and the limiting value of is exactly calculated. Keeping the ratio of the block size and the system size constant, the entanglement entropy exhibits a scaling property, however, the corresponding scaling function may be nonanalytic.