Abstract
Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called A B A B interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3 / 2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity.
Highlights
Entanglement is one of the most characteristic features of quantum mechanics, which provides correlations between objects that are unexplainable in classical mechanics
We introduce large-N matrix models whose correlation functions at the tree and planar level reproduce the square-root scaling of the entanglement entropy (EE) of the Motzkin and Fredkin spin chains
By analyzing the exact solution of one of the matrix models, we find that analogous quantity to the EE
Summary
Entanglement is one of the most characteristic features of quantum mechanics, which provides correlations between objects that are unexplainable in classical mechanics. Let us consider ground states of quantum many-body systems with local interactions Their EEs are proportional to the area of the boundaries of A and B (called as area law [1]). We introduce large-N matrix models whose correlation functions at the tree and planar level reproduce the square-root scaling of the EEs of the Motzkin and Fredkin spin chains. Whereas the tree diagrams are called as rainbow diagrams and look like skeletons [8], loop effects generate diagrams like fishnets that dominate around a critical point and can be regarded as a random surface This gives intuitive understanding of the enhancement of the correlation and the entanglement between the subsystems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
