Portal de Periódicos da CAPES

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

2017; IOP Publishing; Volume: 19; Issue: 3 Linguagem: Inglês

10.1088/1367-2630/aa65bc

1367-2630

Daniel Jaschke, Kenji Maeda, J. D. Whalen, Michael L. Wall, Lincoln D. Carr,

Quantum Computing Algorithms and Architecture

We investigate an extension of the quantum Ising model in one spatial dimension including long-range $1 / r^{\alpha}$ 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 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 quantum Ising model with Matrix Product States. 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 per cent. 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.