Dynamically Tuning One Dimensional Systems Across Quantum Phase Transitions: Classical and Quantal Defects.

Infinite-system time dependent density matrix renormalization group and Loschmidt-amplitude methods are used to analyse the physics occurring when a one dimensional system is dynamically tuned across a quantum phase transition, either by an ac (`Floquet') drive with time vary amplitude or a simple ramp in Hamitloniian parameters. Tuning the XXZ model between two points in the gapped phase introduces classical defects leading to exponentially decaying correlations as expected; tuning between two points in the gapless phase produces excitations which do not destroy the long-distance power-law behavior, and tuning across the phase transition produces quantum phase slips which appear in pairs and then annihilate. Loschmidt methods are used to interrogate the wave function obtained after (one or multiple) ramps across the critical point of the transverse field quantum Ising model, leading to new understanding of the population of the defects created and of the importance of quantum coherence. Portions of this work were performed in collaboration with A. Ron. A. della Torre, D. Hsieh and C. Karrasch.