Krylov state complexity for BMN matrix model

TL;DR

This paper investigates Krylov complexity within the BMN matrix model, utilizing an analytical approach to compute Lanczos coefficients across different deformation regimes.

Contribution

It introduces a systematic reduction to the pulsating fuzzy sphere model and provides analytical calculations of Lanczos coefficients in various limits.

Findings

Analytical expressions for Lanczos coefficients in large and small deformation limits.

Systematic reduction of the BMN matrix model to the pulsating fuzzy sphere model.

Enhanced understanding of Krylov complexity in matrix models.

Abstract

We explore Krylov complexity in the BMN matrix model following a systematic reduction of it, known as the pulsating fuzzy sphere model. We present an analytical setup that allows us to calculate Lanczos coefficients in both large and small deformation limits of the matrix model.