Many-Body Chaos in the Sachdev-Ye-Kitaev Model
| Autor: | Zhenbin Yang, Douglas Stanford, Gregory D. Kahanamoku-Meyer, Bryce Kobrin, Christopher Olund, Norman Y. Yao, Joel E. Moore |
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| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
General Physics General Physics and Astronomy FOS: Physical sciences Lyapunov exponent General Relativity and Quantum Cosmology (gr-qc) 01 natural sciences Mathematical Sciences General Relativity and Quantum Cosmology Many-body problem symbols.namesake Engineering 0103 physical sciences Statistical physics 010306 general physics Quantum Physics Quantum Physics Krylov subspace Fermion MAJORANA Mean field theory High Energy Physics - Theory (hep-th) Quantum Gases (cond-mat.quant-gas) Physical Sciences symbols Hamiltonian (quantum mechanics) Condensed Matter - Quantum Gases Quantum Physics (quant-ph) |
| Zdroj: | Physical Review Letters Physical review letters, vol 126, iss 3 |
| DOI: | 10.48550/arxiv.2002.05725 |
| Popis: | Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev (SYK) model for up to $N = 60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators (OTOCs). We verify that this procedure accurately determines the Lyapunov exponent, $\lambda$, across a wide range in temperatures, including in the regime where $\lambda$ approaches the universal bound, $\lambda = 2\pi/\beta$. Comment: 6+15 pages, 3+11 figures. v3 published version, with corrected prefactor in Eq. 1 |
| Databáze: | OpenAIRE |
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