Quantum Spinodal Phenomena

TL;DR

This paper investigates the rapid magnetization changes in the quantum transverse Ising model, revealing size-independent jumps akin to spinodal decomposition, and introduces a perturbation theory framework for understanding local cluster flips.

Contribution

It presents a novel analysis of fast-sweep magnetization dynamics in the quantum Ising model, linking it to classical spinodal phenomena and developing a perturbation scheme based on Landau-Zener processes.

Findings

Size-independent magnetization jumps observed in fast-sweep regime.

Perturbation theory based on interacting Landau-Zener processes successfully describes local cluster flips.

Analogies drawn between quantum spinodal phenomena and classical phase decomposition.

Abstract

We study the dynamical magnetization process in the ordered ground-state phase of the transverse Ising model under sweeps of magnetic field with constant velocities. In the case of very slow sweeps and for small systems studied previously (Phys. Rev. B 56, 11761 (1997)), non-adiabatic transitions at avoided level-crossing points give the dominant contribution to the shape of magnetization process. In contrast, in the ordered phase of this model and for fast sweeps, we find significant, size-independent jumps in the magnetization process. We study this phenomenon in analogy to the spinodal decomposition in classical ordered state and investigate its properties and its dependence on the system parameters. An attempt to understand the magnetization dynamics under field sweep in terms of the energy-level structure is made. We discuss a microscopic mechanism of magnetization dynamics from a viewpoint of local cluster flips and show that this provides a picture that explains the size independence. The magnetization dynamics in the fast-sweep regime is studied by perturbation theory and we introduce a perturbation scheme based on interacting Landau-Zener type processes to describe the local cluster flip dynamics.