2009/12/31 by Scott D. Geraedts, Scott D Geraedts, Erik S. Sorensen +1
Computer Science · Materials Science · Physics and Astronomy · #Bipartite graph #Boundary (topology) #Chain (unit) #Entropy (arrow of time) #Limit (mathematics) #Multipartite entanglement #Organic and Molecular Conductors Research #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Squashed entanglement #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/43/18/185304
published as J. Phys. A 43, 185304 (2010) · 11 pages, 3 figures
openalex publication_date 2010/04/16 · arxiv created 2010/05/07 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the bipartite entanglement between a subsystem of size l and the rest of the system of total size L as it occurs in a spin-1 Affleck–Kennedy–Lieb–Tasaki (AKLT) chain subject to open boundary conditions. In this case, the ground-state manifold is four-fold degenerate and there is strong dependence on the parity of the number of spins, L . We present exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the subsystem, l , and the total system size, L , for all four degenerate ground states for both odd and even L . In the large l , L limits the entanglement entropy approaches ln (2) for the S z T = ±1 while it approaches twice that value, 2ln (2), for the S z T = 0 states. In all cases, it is found that this constant is approached exponentially fast defining a length scale ξ = 1/ln (3) equal to the known bulk correlation length.