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

TL;DR

This paper provides an exact analytical calculation of the entanglement spectra in matrix product states, specifically for the ground states of q-deformed AKLT and related spin chains, revealing how anisotropy influences entanglement.

Contribution

It introduces a compact, exact formula for the reduced density matrix of MPS, enabling detailed analytic studies of entanglement in anisotropic spin models.

Findings

Entanglement spectra depend on anisotropy parameters.

Constructed an effective boundary spin model with temperature related to q.

Analyzed how deformation affects entanglement properties.

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.