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A. I. Larkin and Y. N. Ovchinnikov, Sov. Phys. JETP 28
1969
Earlier work this paper cites.
E. H. Lieb and D. W. Robinson, Commun. Math. Phys. 28
1972
Earlier work this paper cites.
W. Israel, Phys. Lett. A 57
1976
Earlier work this paper cites.
C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40
1989
Earlier work this paper cites.
S. Sachdev and J. Ye, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
J. M. Maldacena, Int. J. Theor. Phys. 38
1997
Earlier work this paper cites.
E. Witten, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. Gubser, I. Klebanov, and A. Polyakov, Phys. Lett. B 428
1998
Earlier work this paper cites.
O. Parcollet, A. Georges, G. Kotliar, and A. Sengupta, Phys. Rev. B 58
1998
Earlier work this paper cites.
T. D. Kühner, S. R. White, and H. Monien, Phys. Rev. B 61
2000
Earlier work this paper cites.
D. Jaksch and P. Zoller, Ann. Phys. (N. Y). 315
2005
Earlier work this paper cites.
M. B. Hastings and T. Koma, Commun. Math. Phys. 265
2006
Earlier work this paper cites.
B. Nachtergaele and R. Sims, Commun. Math. Phys. 265
2006
Earlier work this paper cites.
I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80
Original
2008
Earlier work this paper cites.
Y. Kato, Q. Zhou, N. Kawashima, and N. Trivedi, Nat. Phys. 4
2008
Earlier work this paper cites.

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2016

Shen, Huitao, Zhang, Pengfei, Fan, Ruihua et al.

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 $2\pi/\beta$ 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 R\'enyi 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.

A. I. Larkin and Y. N. Ovchinnikov, Sov. Phys. JETP 28
1969
Earlier work this paper cites.
E. H. Lieb and D. W. Robinson, Commun. Math. Phys. 28
1972
Earlier work this paper cites.
W. Israel, Phys. Lett. A 57
1976
Earlier work this paper cites.
C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40
1989
Earlier work this paper cites.
S. Sachdev and J. Ye, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
J. M. Maldacena, Int. J. Theor. Phys. 38
1997
Earlier work this paper cites.
E. Witten, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. Gubser, I. Klebanov, and A. Polyakov, Phys. Lett. B 428
1998
Earlier work this paper cites.
O. Parcollet, A. Georges, G. Kotliar, and A. Sengupta, Phys. Rev. B 58
1998
Earlier work this paper cites.
T. D. Kühner, S. R. White, and H. Monien, Phys. Rev. B 61
2000
Earlier work this paper cites.
D. Jaksch and P. Zoller, Ann. Phys. (N. Y). 315
2005
Earlier work this paper cites.
M. B. Hastings and T. Koma, Commun. Math. Phys. 265
2006
Earlier work this paper cites.
B. Nachtergaele and R. Sims, Commun. Math. Phys. 265
2006
Earlier work this paper cites.
I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80
Original
2008
Earlier work this paper cites.
Y. Kato, Q. Zhou, N. Kawashima, and N. Trivedi, Nat. Phys. 4
2008
Earlier work this paper cites.