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 bn 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 \( \sim \exp \left(\mathcal{O}\left(\sqrt{t}\right)\right) \). These results indicate that the IP model at sufficiently high temperature is chaotic.
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Acknowledgments
We are happy to thank Pratik Nandy for his helpful conversations at several stages and comments on the draft. We also thank him for his Mathematica code sharing with us. The work of NI was supported in part by JSPS KAKENHI Grant Number 18K03619 and also by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas A “Extreme Universe” No. 21H05184. M.N. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1I1A1A01072726). M.N. carried out part of this work while visiting Osaka University and would like to thank Osaka University for its hospitality and support.
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Iizuka, N., Nishida, M. Krylov complexity in the IP matrix model. J. High Energ. Phys. 2023, 65 (2023). https://doi.org/10.1007/JHEP11(2023)065
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DOI: https://doi.org/10.1007/JHEP11(2023)065