Deformed Fredkin spin chain with extensive entanglement. (15th June 2017)

• Record Type: Journal Article
• Authors: Salberger, Olof; Udagawa, Takuma; Zhang, Zhao; Katsura, Hosho; Klich, Israel; Korepin, Vladimir
• Is Part Of: Journal of statistical mechanics. (2017:Jun.)
• Publication Date: 2017-06-15
• Subjects: 2 -- 1; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa6b1f
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors. The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths that depends on a deformation parameter t . In the purely spin 1/2 case, whenever t ≠ 1, the entanglement entropy obeys an area law: it is bounded from above by a constant, when the size of the block n increases. When a local color degree of freedom is introduced and t > 1 the entanglement entropy increases linearly, while for t < 1 an area law is obeyed. The half-chain entanglement entropy is tightly bounded by n log ⁡ s where 2 n is the length of the chain, and s is the number of colors. Our chain fosters a new example for a significant boost to entropy and for the existence of the associated critical rainbow phase where the entanglement entropy scales with volume that discovered by Zhang, Ahmadain and Klich ( Proc. Natl Acad. Sci 2017).