Krylov complexity in the IP matrix model

• URL: http://arxiv.org/abs/2306.04805v1
• Date: Wed, 7 Jun 2023 21:58:09 GMT
• Title: Krylov complexity in the IP matrix model
• Authors: Norihiro Iizuka, Mitsuhiro Nishida
• Abstract summary: The IP matrix model is a simple large $N$ quantum mechanical model made up of an adjoint harmonic oscillator plus a fundamental harmonic oscillator. We study the Lanczos coefficients $b_n$ in this model and at sufficiently high temperature, it grows linearly in $n$ with logarithmic corrections. As a result, the Krylov complexity grows exponentially in time as $sim expleft(calOleft(sqrttright)right.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\sim \exp\left({{\cal{O}}{\left(\sqrt{t}\right) }}\right)$. These results indicate that the IP model at sufficiently high temperature is chaotic.

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