Abstract
Motzkin and Fredkin spin chains are new spin chain models exhibiting extraordinary amount of entanglement entropy scaling as a square root of the volume in spite of local interactions. This is a distinguished feature of the models from other spin chains with entanglement of at most logarithmic scaling. We first compute generalized entanglement entropy, called as the Rényi entropy, of these models. The Rényi entropy has further importance, since it can provide the whole spectrum of an entangled subsystem. We find non-analytic behavior of the Rényi entropy that can be regarded as a phase transition never seen in any other spin chain investigated so far. This new phase transition indicates unique and rich structures of the entanglement spectrum.
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Notes
- 1.
Although the analysis for the case \(r=0\) is already given in [20], we briefly present the derivation to make this article self-contained as much as possible.
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Sugino, F., Korepin, V. (2020). Generalized Entanglement Entropy in New Spin Chains. In: Ferraz, A., Gupta, K., Semenoff, G., Sodano, P. (eds) Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory. Springer Proceedings in Physics, vol 239. Springer, Cham. https://doi.org/10.1007/978-3-030-35473-2_4
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