Critical phenomena and Kibble–Zurek scaling in the long-range quantum Ising chain. (27th March 2017)

• Record Type: Journal Article
• Authors: Jaschke, Daniel; Maeda, Kenji; Whalen, Joseph D; Wall, Michael L; Carr, Lincoln D
• Is Part Of: New journal of physics. Volume 19:Number 3(2017:Mar.)
• Publication Date: 2017-03-27
• Subjects: long-range quantum Ising -- entangled quantum dynamics -- Kibble–Zurek scaling -- matrix product states -- trapped ion arrays -- ultracold molecules and Rydberg gases -- quantum simulators; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/aa65bc
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: We investigate an extension of the quantum Ising (QI) model in one spatial dimension including long-range 1 / r α 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.