Adiabatic dynamics in passage across quantum critical lines and gapless phases

TL;DR

This paper explores conditions under which quantum systems can undergo adiabatic passage through critical regions, resulting in exponential decay of defect density, contrasting the typical power-law scaling at quantum critical points.

Contribution

It introduces a scenario where additional interactions enable adiabatic dynamics across quantum critical regions without defect accumulation, supported by analysis of an extended XY spin chain.

Findings

Defect density decays exponentially under certain conditions

Additional interactions can decouple critical behavior from dynamics

The model demonstrates adiabatic passage across quantum critical regions

Abstract

It is well known that the dynamics of a quantum system is always non-adiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system. To illustrate the general argument, we study the defect generation in the quantum critical dynamics of a spin-1/2 anisotropic quantum XY spin chain with three spin interactions and a linearly driven staggered magnetic field.