2018/11/29 by Rafael N. Alexander, Amr Ahmadain, Zhao Zhang +1 · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.100.214430
published as Phys. Rev. B 100, 214430 (2019) · 7 pages, 6 figures
arxiv created 2018/11/29 · arxiv updated 2020/01/01
We present bulk tensor networks that exactly represent the ground states of a continuous family of one-dimensional frustration-free Hamiltonians. These states, which are known as area-deformed Motzkin and Fredkin states, exhibit a novel quantum phase transition. By tuning a single parameter, they go from a phase obeying an area law to a highly entangled rainbow phase, where the half-chain entropy scales with the volume. Using the representation of these ground states as superpositions of random walks, we introduce tensor networks for these ground states where local and global rules of the walker are baked into bulk tensors, thereby providing an efficient description of the ground states (some of which satisfy a volume law scaling of entanglement entropy).