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 s >= 2 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, s >= 3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy. © 2016 American Physical Society.

Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains / Dell'Anna, L.; Salberger, O.; Barbiero, L.; Trombettoni, Andrea; Korepin, V. E.. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - 94:15(2016), pp. 155140.1-155140.9. [10.1103/PhysRevB.94.155140]

Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains

Trombettoni, Andrea;
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 s >= 2 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, s >= 3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy. © 2016 American Physical Society.
94
15
1
9
155140
https://arxiv.org/abs/1604.08281
http://cdsads.u-strasbg.fr/abs/2016PhRvB..94o5140D
Dell'Anna, L.; Salberger, O.; Barbiero, L.; Trombettoni, Andrea; Korepin, V. E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/33276
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