Local Quenches from a Krylov Perspective

TL;DR

This paper explores local quench dynamics in 2D conformal field theories using Krylov space methods, revealing how complexity measures relate to central charge and holography, and demonstrating their utility in non-equilibrium quantum systems.

Contribution

It introduces Krylov space techniques to analyze local quenches in 2D CFTs, linking complexity measures to central charge and holographic duals, and highlights their effectiveness in studying quantum dynamics.

Findings

Spread complexity and Krylov entropy are proportional to the central charge.

Krylov entropies grow logarithmically with time, similar to entanglement entropy.

Holographic analysis connects spread complexity rate to brane momentum.

Abstract

In this work, we investigate local quench dynamics in two-dimensional conformal field theories using Krylov space methods. We derive Lanczos coefficients, spread complexity, and Krylov entropies for local joining and splitting quenches in theories on an infinite line, a circle, a finite interval, and at finite temperature. We examine how these quantities depend on the central charge of the underlying conformal field theory and find that both spread complexity and Krylov entropy are proportional to it. Interestingly, Krylov entropies evolve logarithmically with time, mirroring standard entanglement entropies, making them useful for extracting the central charge. In the large central charge limit, using holography, we establish a connection between the rate of spread complexity and the proper momentum of the tip of the end-of-the world brane, which probes the bulk analogously to a point particle. Our results further demonstrate that spread complexity and Krylov entropies are powerful tools for probing non-equilibrium dynamics of interacting quantum systems.