Entanglement spectra of the q-deformed Affleck-Kennedy-Lieb-Tasaki model and matrix product states

2011/12/31 by Raul A. Santos, Francis N. C. Paraan, V. E. Korepin +2
Mathematics · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #math.QA #quant-ph

paper · pdf · doi:10.1209/0295-5075/98/37005

published as Europhys. Lett., 98 (2012) 37005 · 5 pages, 4 PDF figures; v2: 6 pages, 4 PDF figures. Introduction and conclusions expanded

openalex publication_date 2012/05/01 · arxiv created 2012/05/14 · arxiv updated 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

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 .

Citations

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