Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states
C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook Stony Brook, NY 11794-3840, USA
2 Fachbereich C Physik, Bergische Universität Wuppertal - 42097 Wuppertal, Germany, EU
Accepted: 13 April 2012
We exactly calculate the reduced density matrix of matrix product states (MPS). Our compact result enables one to perform analytic studies of entanglement in MPS. In particular, we consider the MPS ground states of two anisotropic spin chains. One is a q-deformed Affleck-Kennedy-Lieb-Tasaki (AKLT) model and the other is a general spin-1 quantum antiferromagnet with nearest-neighbor interactions. Our analysis shows how anisotropy affects entanglement on different continuous parameter manifolds. We also construct an effective boundary spin model that describes a block of spins in the ground state of the q-deformed AKLT Hamiltonian. The temperature of this effective model is given in terms of the deformation parameter q.
PACS: 75.10.Pq – Spin chain models / 75.10.Jm – Quantized spin models, including quantum spin frustration / 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)
© EPLA, 2012