Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies

Abstract

We study the geometrical entanglement of the XXZ chain in its critical regime. Recent numerical simulations [Q.-Q. Shi, R. Orús, J. O. Fjærestad and H.-Q Zhou, New J. Phys. {\bf 12}, 025008 (2010)] indicate that it scales linearly with system size, and that the first subleading correction is constant, which was argued to be possibly universal. In this work, we confirm the universality of this number, by relating it to the Affleck-Ludwig boundary entropy corresponding to a Neumann boundary condition for a free compactified field. We find that the subleading constant is a simple function of the compactification radius, in agreement with the numerics. As a further check, we compute it exactly on the lattice at the XX point. We also discuss the case of the Ising chain in transverse field and show that the geometrical entanglement is related to the Affleck-Ludwig boundary entropy associated to a ferromagnetic boundary condition.

4 pages, 1 figure

References in corpus (4)

• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Universal geometric entanglement close to quantum phase transitions
• Rényi entropy of a line in two-dimensional Ising models
• Fundamentals of universality in one-way quantum computation

Cited by in corpus (4)

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• Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain
• Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
• Entanglement Properties of a Higher-Integer-Spin AKLT Model with Quantum Group Symmetry