Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields

TL;DR

This paper shows that inhomogeneous driving fields can counteract disorder effects in transverse-field Ising chains, restoring algebraic scaling of defect density during quantum critical point traversals.

Contribution

It introduces a method to balance disorder with inhomogeneous fields, achieving algebraic defect scaling in disordered quantum chains, a novel approach in quantum critical dynamics.

Findings

Balancing disorder with inhomogeneous fields restores algebraic defect scaling.

Perfect balancing yields the inverse-square law of defect density.

Partial balancing still improves defect scaling with a non-universal exponent.

Abstract

In transverse-field Ising models, disorder in the couplings gives rise to a drastic reduction of the critical energy gap and, accordingly, to an unfavorable, slower-than-algebraic scaling of the density of defects produced when the system is driven through its quantum critical point. By applying Kibble-Zurek theory and numerical calculations, we demonstrate in the one-dimensional model that the scaling of defect density with annealing time can be made algebraic by balancing the coupling disorder with suitably chosen inhomogeneous driving fields. Depending on the tail of the coupling distribution at zero, balancing can be either perfect, leading to the well-known inverse-square law of the homogeneous system, or partial, still resulting in an algebraic decrease but with a smaller, non-universal exponent. We also study defect production during an environment-temperature quench of the open variant of the model in which the system is slowly cooled down to its quantum critical point. According to our scaling and numerical results, balanced disorder leads again to an algebraic temporal decrease of the defect density.