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

TL;DR

This paper explores how the Kibble-Zurek mechanism reveals universal and subleading critical exponents in quantum phase transitions, using the transverse XY model and analytical solutions to understand the effects of different driving protocols.

Contribution

It demonstrates how driving various couplings in the transverse XY model activates the full spectrum of critical exponents, including subleading ones, through analytical and experimental insights.

Findings

Subleading exponents can be observed via tailored driving protocols.

Driving parallel to the phase boundary reveals subleading exponents clearly.

Universal scaling behavior is influenced by non-universal model content.

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.