Renyi entropy of highly entangled spin chains

Abstract

Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an "area law" meaning the entanglement entropy proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm for over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. Although importance of intensive study of the models is undoubted to reveal novel features of quantum entanglement, it is still far from their complete understanding. In this article, we first analytically compute the Renyi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The Renyi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the Renyi entropy is known as a function of its parameter. We find non-analytic behavior of the Renyi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin chain studied so far. Interestingly, similar behavior is seen in the Renyi entropy of Rokhsar-Kivelson states in two-dimensions.

14+22 pages, 8 figures; (v2) references added, (v3) version to be published in International Journal of Modern Physics B

References in corpus (3)

• Gapless quantum spin chains: multiple dynamics and conformal wavefunctions
• Entanglement and Density Matrix of a Block of Spins in AKLT Model
• The pair-flip model: a very entangled translationally invariant spin chain

Cited by in corpus (12)

• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Entanglement as geometry and flow
• Unusual area-law violation in random inhomogeneous systems
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Long-distance entanglement in Motzkin and Fredkin spin chains
• Holographic Entanglement Entropy of the Coulomb Branch
• Non-thermal eigenstates and slow relaxation in quantum Fredkin spin chains
• Dynamics and correlations in Motzkin and Fredkin spin chains
• Tunable quantum spin chain with three-body interactions
• Heisenberg XX chain, non-homogeneously parameterised generating exponential, and diagonally restricted plane partitions
• Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions
• Highly entangled spin chains and 2D quantum gravity