Robustness of adiabatic passage trough a quantum phase transition

Abstract

We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field is tuned through the critical point with a linear ramping. The excitation probability is obtained exactly and is compared to previous studies and to the Landau-Zener formula, a long time solution for non-adiabatic transitions in two-level systems. The exact time dependence of the excitations density in the system allows to identify the adiabatic and diabatic regions during the sweep and to study the mesoscopic fluctuations of the excitations. The effect of white noise is investigated, where the critical point transmutes into a non-hermitian ``degenerate region''. Besides an overall increase of the excitations during and at the end of the sweep, the most destructive effect of the noise is the decay of the state purity that is enhanced by the passage through the degenerate region.

16 pages, 15 figures

References in corpus (2)

• Universal adiabatic dynamics across a quantum critical point
• Noise resistance of adiabatic quantum computation using random matrix theory

Cited by in corpus (6)

• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Optimal non-linear passage through a quantum critical point
• Phase Transition in Space: How Far Does a Symmetry Bend Before It Breaks?
• Decoherence in the dynamical quantum phase transition of the transverse Ising chain
• Adiabatic preparation without Quantum Phase Transitions