Krylov complexity in the IP matrix model

DOI10.1007/JHEP11(2023)065arXiv2306.04805OpenAlexW4388599230MaRDI QIDQ6183416

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Publication date: 26 January 2024

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Abstract: The IP matrix model is a simple large $N$ quantum mechanical model made up of an adjoint harmonic oscillator plus a fundamental harmonic oscillator. It is a model introduced previously as a toy model of the gauge theory dual of an AdS black hole. In the large $N$ limit, one can solve the Schwinger-Dyson equation for the fundamental correlator, and at sufficiently high temperature, this model shows key signatures of thermalization and information loss; the correlator decay exponentially in time, and the spectral density becomes continuous and gapless. We study the Lanczos coefficients $b_n$ in this model and at sufficiently high temperature, it grows linearly in $n$ with logarithmic corrections, which is one of the fastest growth under certain conditions. As a result, the Krylov complexity grows exponentially in time as $simexpleft(calOleft(sqrttight)ight)$. These results indicate that the IP model at sufficiently high temperature is chaotic.

Full work available at URL: https://arxiv.org/abs/2306.04805

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