Crossover from Classical to Quantum Kibble-Zurek Scaling

Abstract

The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a φ 4 model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and to the classical case. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to provide insight into recent experimental observations in systems of cold atoms and ions.

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

“…Within this simplified picture, the transition between the two stages is supposed to be sharp at a certain value of the external parameter which sets the length scale of the correlations in the final state. The scaling laws predicted by the adiabatic-impulse approximation have been investigated theoretically in a number of classical settings [18][19][20][21][22][23][24] and found to be in good agreement with experimental results [25][26][27][28][29]. The quantum Kibble-Zurek (QKZ) scaling laws, on the other hand, have been studied in [10][11][12][13]24].…”

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

“…[24] for a review). When the annealing velocity is progressively increased, crossover behaviour sets in between the KZ scaling and the generation of excitations due to faster quenches, where the dynamics can be described by the underlying classical model [25]. The proliferation of defects due to Landau-Zener transitions is intimately related to the occurrence of errors in the AQC, while in the unitary case, the number of defects decreases upon increasing the annealing time, and the environment will be dominant for long annealing times.…”

Realization of Translational Symmetry in Trapped Cold Ion Rings

“…Our experiment paves the way towards studying quantum many-body physics with translational symmetry at the single particle level in a variety of disciplines from simulation of Hawking radiation [13] to exploration of quantum phase transitions [14]. In addition, the ring geometry enables novel opportunities to study diverse topics including dynamics of kink solitons [15,16], the Kibble-Zureck mechanism [17][18][19], the Aharanov-Bohm effect [20], symmetry breaking with indistinguishable particles [21,22], frequency metrology [23], quantum friction [24], and quantum computation [25].…”