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arXiv · 1811.11974

Holographic rainbow networks for colorful Motzkin and Fredkin spin chains

Rafael N. Alexander·Amr Ahmadain·Zhao Zhang·Israel Klich
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Abstract

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).

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Rafael N. Alexander, Amr Ahmadain, Zhao Zhang, Israel Klich. 2018-11-29. Holographic rainbow networks for colorful Motzkin and Fredkin spin chains. https://doi.org/10.1103/physrevb.100.214430

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