Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains

L. Dell'Anna, O. Salberger, L. Barbiero, A. Trombettoni, and V. E. Korepin
Phys. Rev. B 94, 155140 – Published 25 October 2016

Abstract

We compute the ground-state correlation functions of an exactly solvable chain of integer spins, recently introduced in [R. Movassagh and P. W. Shor, arXiv:1408.1657], whose ground state can be expressed in terms of a uniform superposition of all colored Motzkin paths. Our analytical results show that for spin s2 there is a violation of the cluster decomposition property. This has to be contrasted with s=1, where the cluster property holds. Correspondingly, for s=1 one gets a light-cone profile in the propagation of excitations after a local quench, while the cone is absent for s=2, as shown by time dependent density-matrix renormalization group. Moreover, we introduce an original solvable model of half-integer spins, which we refer to as Fredkin spin chain, whose ground state can be expressed in terms of superposition of all Dyck paths. For this model we exactly calculate the magnetization and correlation functions, finding that for s=1/2, a conelike propagation occurs, while for higher spins, s3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy.

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  • Received 6 May 2016
  • Revised 13 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.155140

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

L. Dell'Anna1, O. Salberger2, L. Barbiero1,3, A. Trombettoni3,4, and V. E. Korepin2

  • 1Dipartimento di Fisica e Astronomia “G. Galilei,” Università di Padova, via F. Marzolo 8, I-35131 Padova, Italy
  • 2C. N. Yang Institute for Theoretical Physics, Stony Brook University, New York 11794, USA
  • 3CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy
  • 4SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy

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Issue

Vol. 94, Iss. 15 — 15 October 2016

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