2016/08/31 by Huitao Shen, Pengfei Zhang, Ruihua Fan +1 · 1 citation
Physics and Astronomy · #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.96.054503
published as Phys. Rev. B 96, 054503 (2017) · 7 pages, 6 figures, published version
arxiv created 2017/08/17 · arxiv updated 2017/08/21
In this paper we numerically calculate the out-of-time-order correlation functions in the one-dimensional Bose-Hubbard model. Our study is motivated by the conjecture that a system with Lyapunov exponent saturating the upper bound 2π/β will have a holographic dual to a black hole at finite temperature. We further conjecture that for a many-body quantum system with a quantum phase transition, the Lyapunov exponent will have a peak in the quantum critical region where there exists an emergent conformal symmetry and is absent of well-defined quasi-particles. With the help of a relation between the Rényi entropy and the out-of-time-order correlation function, we argue that the out-of-time-order correlation function of the Bose-Hubbard model will also exhibit an exponential behavior at the scrambling time. By fitting the numerical results with an exponential function, we extract the Lyapunov exponents in the one-dimensional Bose-Hubbard model across the quantum critical regime at finite temperature. Our results on the Bose-Hubbard model support the conjecture. We also compute the butterfly velocity and propose how the echo type measurement of this correlator in the cold atom realizations of the Bose-Hubbard model without inverting the Hamiltonian.