Critical phenomena and Kibble-Zurek scaling in the long-range quantum Ising chain

We investigate an extension of the quantum Ising (QI) model in one spatial dimension including long-range 1 r interactions in its statics and dynamics with possible applications from heteronuclear polar molecules in optical lattices to trapped ions described by two-state spin systems. We introduce t...

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Bibliographic Details
Published in:	New journal of physics 2017-03, Vol.19 (3), p.33032
Main Authors:	Jaschke, Daniel, Maeda, Kenji, Whalen, Joseph D, Wall, Michael L, Carr, Lincoln D
Format:	Article
Language:	eng
Subjects:	Antiferromagnetism Critical phenomena Critical point Density entangled quantum dynamics Ferromagnetism Ising model Kibble-Zurek scaling long-range quantum Ising Mathematical models matrix product states Optical lattices Physics quantum simulators Size effects trapped ion arrays ultracold molecules and Rydberg gases
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Summary:	We investigate an extension of the quantum Ising (QI) model in one spatial dimension including long-range 1 r interactions in its statics and dynamics with possible applications from heteronuclear polar molecules in optical lattices to trapped ions described by two-state spin systems. We introduce the statics of the system via both numerical techniques with finite size and infinite size matrix product states (MPSs) and a theoretical approaches using a truncated Jordan-Wigner transformation for the ferromagnetic and antiferromagnetic case and show that finite size effects have a crucial role shifting the quantum critical point of the external field by fifteen percent between thirty-two and around five-hundred spins. We numerically study the Kibble-Zurek hypothesis in the long-range QI model with MPSs. A linear quench of the external field through the quantum critical point yields a power-law scaling of the defect density as a function of the total quench time. For example, the increase of the defect density is slower for longer-range models and the critical exponent changes by twenty-five percent. Our study emphasizes the importance of such long-range interactions in statics and dynamics that could point to similar phenomena in a different setup of dynamical systems or for other models.
ISSN:	1367-2630 1367-2630