Krylov Complexity Meets Confinement

TL;DR

This paper demonstrates that Krylov state complexity effectively detects confinement phenomena in the Ising model, revealing distinct complexity growth patterns and oscillations linked to meson masses, thus providing a quantum information perspective on confinement.

Contribution

It introduces Krylov state complexity as a novel quantitative probe for confinement in condensed matter systems, connecting quantum information measures with high-energy physics phenomena.

Findings

Confinement suppresses Krylov complexity growth after quenches in the ferromagnetic phase.

Enhanced complexity observed in the paramagnetic phase with increasing longitudinal field.

Complexity oscillations at meson mass frequencies match semiclassical predictions.

Abstract

In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed matter systems, for instance, in the Ising model with both transverse and longitudinal fields, where domain walls become confined into meson-like bound states as a result of a longitudinal field-induced linear potential. In this work, we employ the Ising model to demonstrate that Krylov state complexity--a measure quantifying the spread of quantum information under the repeated action of the Hamiltonian on a quantum state--serves as a sensitive and quantitative probe of confinement. We show that confinement manifests as a pronounced suppression of Krylov complexity growth following quenches within the ferromagnetic phase in the presence of a longitudinal field, reflecting slow correlation dynamics. In contrast, while quenches within the paramagnetic phase exhibit enhanced complexity with increasing longitudinal field, reflecting the absence of confinement, those crossing the critical point to the ferromagnetic phase reveal a distinct regime characterized by orders-of-magnitude larger complexity and display trends of weak confinement. Notably, in the confining regime, the complexity oscillates at frequencies corresponding to the meson masses, with its power-spectrum peaks closely matching the semiclassical predictions.