Built on

R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugen. 7
1937
Earlier work this paper cites.
A. Kolmogorov, I. Petrovsky, and N. Piscounov, A study of the diffusion equation with increase in the amount of substance, Bull. Univ. État Moscou 1
1937
Earlier work this paper cites.
M. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Am. Math. Soc. 44
1983
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J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43
1991
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S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50
1994
Earlier work this paper cites.
E. Brunet and B. Derrida, Shift in the velocity of a front due to a cutoff, Phys. Rev. E 56
1997
Earlier work this paper cites.
H. Tasaki, From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example, Phys. Rev. Lett. 80
1998
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G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91
2003
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G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93
2004
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E. Brunet, B. Derrida, A. H. Mueller, and S. Munier, Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts, Phys. Rev. E 73
2006
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P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 2007
Original
2007
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Y. Sekino and L. Susskind, Fast scramblers, JHEP 2008
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2008
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M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature 452
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T. H. Johnson, S. R. Clark, and D. Jaksch, Dynamical simulations of classical stochastic systems using matrix product states, Phys. Rev. E 82
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N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, Towards the fast scrambling conjecture, JHEP 2013
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2013
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S. H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 2014
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A. Kitaev, A simple model of quantum holography, in KITP Progr. Entanglement Strongly-Correlated Quantum Matter (2015)
2015
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S. H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 2015
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2015
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P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, Chaos in quantum channels, JHEP 2016
Original
2016
Earlier work this paper cites.

Similar

B. Swingle, G. Bentsen, M. Schleier-Smith, and P. Hayden, Measuring the scrambling of quantum information, Phys. Rev. A 94
Original
2016
Cited alongside, same era.
G. Zhu, M. Hafezi, and T. Grover, Measurement of many-body chaos using a quantum clock, Phys. Rev. A 94
2016
Cited alongside, same era.
N. Y. Yao, F. Grusdt, B. Swingle, M. D. Lukin, D. M. Stamper-Kurn, J. E. Moore, and E. A. Demler, Interferometric Approach to Probing Fast Scrambling, arXiv:1607.01801 (2016)
Original
2016
Cited alongside, same era.
A. Bohrdt, C. B. Mendl, M. Endres, and M. Knap, Scrambling and thermalization in a diffusive quantum many-body system, New J. Phys. 19
Original
2016
Cited alongside, same era.
Y. Chen, Universal Logarithmic Scrambling in Many Body Localization, arXiv:1608.02765 (2016)

Then

Y. Huang, Y.-L. Zhang, and X. Chen, Out-of-time-ordered correlators in many-body localized systems, Ann. Phys. 529
Original
2017
Later among the works it cites.
E. Leviatan, F. Pollmann, J. H. Bardarson, D. A. Huse, and E. Altman, Quantum thermalization dynamics with Matrix-Product States, arXiv:1702.08894 (2017)
Original
2017
Later among the works it cites.
J. Berestycki, É. Brunet, S. C. Harris, and M. Roberts, Vanishing Corrections for the Position in a Linear Model of FKPP Fronts, Commun. Math. Phys. 349
2017
Later among the works it cites.
A. Nahum, S. Vijay, and J. Haah, Operator Spreading in Random Unitary Circuits, Phys. Rev. X 8
Original
2018
Closest in time.
C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws, Phys. Rev. X 8

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2018

Locality, Quantum Fluctuations, and Scrambling

Xu, Shenglong, Swingle, Brian

Understand

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators.

Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs).
However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront.
In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians.

Built on

R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugen. 7
1937
Earlier work this paper cites.
A. Kolmogorov, I. Petrovsky, and N. Piscounov, A study of the diffusion equation with increase in the amount of substance, Bull. Univ. État Moscou 1
1937
Earlier work this paper cites.
M. Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Am. Math. Soc. 44
1983
Earlier work this paper cites.
J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43
1991
Earlier work this paper cites.
S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum Heisenberg magnet, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50
1994
Earlier work this paper cites.
E. Brunet and B. Derrida, Shift in the velocity of a front due to a cutoff, Phys. Rev. E 56
1997
Earlier work this paper cites.
H. Tasaki, From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example, Phys. Rev. Lett. 80
1998
Earlier work this paper cites.
G. Vidal, Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
E. Brunet, B. Derrida, A. H. Mueller, and S. Munier, Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts, Phys. Rev. E 73
2006
Earlier work this paper cites.
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 2007
Original
2007
Earlier work this paper cites.
Y. Sekino and L. Susskind, Fast scramblers, JHEP 2008
Original
2008
Earlier work this paper cites.
M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature 452
2008
Earlier work this paper cites.
T. H. Johnson, S. R. Clark, and D. Jaksch, Dynamical simulations of classical stochastic systems using matrix product states, Phys. Rev. E 82
2010
Earlier work this paper cites.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, Towards the fast scrambling conjecture, JHEP 2013
Original
2013
Earlier work this paper cites.
S. H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 2014
2014
Earlier work this paper cites.
A. Kitaev, A simple model of quantum holography, in KITP Progr. Entanglement Strongly-Correlated Quantum Matter (2015)
2015
Earlier work this paper cites.
S. H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 2015
Original
2015
Earlier work this paper cites.
P. Hosur, X.-L. Qi, D. A. Roberts, and B. Yoshida, Chaos in quantum channels, JHEP 2016
Original
2016
Earlier work this paper cites.

Similar

B. Swingle, G. Bentsen, M. Schleier-Smith, and P. Hayden, Measuring the scrambling of quantum information, Phys. Rev. A 94
Original
2016
Cited alongside, same era.
G. Zhu, M. Hafezi, and T. Grover, Measurement of many-body chaos using a quantum clock, Phys. Rev. A 94
2016
Cited alongside, same era.
N. Y. Yao, F. Grusdt, B. Swingle, M. D. Lukin, D. M. Stamper-Kurn, J. E. Moore, and E. A. Demler, Interferometric Approach to Probing Fast Scrambling, arXiv:1607.01801 (2016)
Original
2016
Cited alongside, same era.
A. Bohrdt, C. B. Mendl, M. Endres, and M. Knap, Scrambling and thermalization in a diffusive quantum many-body system, New J. Phys. 19
Original
2016
Cited alongside, same era.
Y. Chen, Universal Logarithmic Scrambling in Many Body Localization, arXiv:1608.02765 (2016)

Then

Y. Huang, Y.-L. Zhang, and X. Chen, Out-of-time-ordered correlators in many-body localized systems, Ann. Phys. 529
Original
2017
Later among the works it cites.
E. Leviatan, F. Pollmann, J. H. Bardarson, D. A. Huse, and E. Altman, Quantum thermalization dynamics with Matrix-Product States, arXiv:1702.08894 (2017)
Original
2017
Later among the works it cites.
J. Berestycki, É. Brunet, S. C. Harris, and M. Roberts, Vanishing Corrections for the Position in a Linear Model of FKPP Fronts, Commun. Math. Phys. 349
2017
Later among the works it cites.
A. Nahum, S. Vijay, and J. Haah, Operator Spreading in Random Unitary Circuits, Phys. Rev. X 8
Original
2018
Closest in time.
C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws, Phys. Rev. X 8

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2016

Cited alongside, same era.

I. L. Aleiner, L. Faoro, and L. B. Ioffe, Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves, Ann. Phys. (N. Y). 375

Original

2016

Cited alongside, same era.

J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, JHEP 2016

2016

Cited alongside, same era.

N. Yunger Halpern, Jarzynski-like equality for the out-of-time-ordered correlator, Phys. Rev. A 95

Original

2017

Cited alongside, same era.

M. Campisi and J. Goold, Thermodynamics of quantum information scrambling, Phys. Rev. E 95

Original

2017

Cited alongside, same era.

B. Yoshida and A. Kitaev, Efficient decoding for the Hayden-Preskill protocol, arXiv:1710.03363 (2017)

Original

2017

Cited alongside, same era.

M. Garttner, J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M. Rey, Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet, Nat. Phys. 13

Original

2017

Cited alongside, same era.

J. Li, R. Fan, H. Wang, B. Ye, B. Zeng, H. Zhai, X. Peng, and J. Du, Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator, Phys. Rev. X 7

2017

Cited alongside, same era.

Original

2018

Closest in time.

S. Xu and B. Swingle, Accessing scrambling using matrix product operators, arXiv:1802.00801 (2018)

Original

2018

Closest in time.

D. A. Roberts, D. Stanford, and A. Streicher, Operator growth in the SYK model, JHEP 2018

Original

2018