2023/08/15 by Norihiro Iizuka, Iizuka, Norihiro, Mitsuhiro Nishida +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #Quantum many-body systems #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2308.07567
openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue the analysis of the Krylov complexity in the IP matrix model. In a previous paper, for a fundamental operator, it was shown that at zero temperature, the Krylov complexity oscillates and does not grow, but in the infinite temperature limit, the Krylov complexity grows exponentially in time as ∼ exp( O( √(t)) ). We study how the Krylov complexity changes from a zero-temperature oscillation to an infinite-temperature exponential growth. At low temperatures, the spectral density is approximated as collections of infinite Wigner semicircles. We showed that this infinite collection of branch cuts yields linear growth to the Lanczos coefficients and gives exponential growth of the Krylov complexity. Thus the IP model for any nonzero temperature shows exponential growth for the Krylov complexity even though the Green function decays by a power law in time. We also study the Lanczos coefficients and the Krylov complexity in the IOP matrix model taking into account the 1/N2 corrections. There, the Lanczos coefficients are constants and the Krylov complexity does not grow exponentially as expected.