Kibble-Zurek mechanism from different angles: The transverse XY model and subleading scalings

Abstract

The Kibble-Zurek mechanism describes the saturation of critical scaling upon dynamically approaching a phase transition. This is a consequence of the breaking of adiabaticity due to the scale set by the slow drive. By driving the gap parameter, this can be used to determine the leading critical exponents. But this is just the `tip of the iceberg': Driving more general couplings allows one to activate the entire universal spectrum of critical exponents. Here we establish this phenomenon and its observable phenomenology for the quantum phase transitions in an analytically solvable minimal model and the experimentally relevant transverse XY model. The excitation density is shown to host the sequence of exponents including the subleading ones in the asymptotic scaling behavior by a proper design of the geometry of the driving protocol in the phase diagram. The case of a parallel drive relative to the phase boundary can still lead to the breaking of adiabaticity, and exposes the subleading exponents in the clearest way. Complementarily to disclosing universal information, we extract the restrictions due to the non-universal content of the models onto the extent of the subleading scalings regimes.

References in corpus (20)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Universal adiabatic dynamics across a quantum critical point
• Dynamical phase transition in the open Dicke model
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Quench-induced supercurrents in an annular Bose gas
• Defect production in non-linear quench across a quantum critical point
• Emergence of coherence and the dynamics of quantum phase transitions
• Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics
• Observation of Solitonic Vortices in Bose-Einstein Condensates
• Optimal non-linear passage through a quantum critical point
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Quenching along a gapless line: A different exponent for defect density
• Defect production due to quenching through a multicritical point
• Theory of defect production in nonlinear quench across a quantum critical point
• Exploring the Kibble-Zurek mechanism with homogeneous Bose gases
• Realization of inverse Kibble-Zurek scenario with trapped Bose gases
• Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching
• Domain dynamics in LiCuVO${}_4$: Evidence for polarized nanoregions