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

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.

5 pages, 4 PDF figures; v2: 6 pages, 4 PDF figures. Introduction and conclusions expanded

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Cited by in corpus (13)

• Quantum entanglement in condensed matter systems
• Entanglement of Exact Excited States of AKLT Models: Exact Results, Many-Body Scars and the Violation of Strong ETH
• Dynamics of the entanglement spectrum in spin chains
• Calculating statistical distributions from operator relations: the statistical distributions of various intermediate statistics
• Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Graph states as ground states of two-body frustration-free Hamiltonians
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states
• Schmidt gap in random spin chains
• Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models
• Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry
• Entanglement-fluctuation relation for bipartite pure states
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model