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A. Schuckert and M. Knap, Many-body chaos near a thermal phase transition, SciPost Phys. 7
Original
1905
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, JETP 28
1969
Earlier work this paper cites.
M. V. Berry, and M. Tabor, Level clustering in the regular spectrum, Proc. Roy. Soc. A 356
1977
Earlier work this paper cites.
G. Casati, F. Valz-Gris, and I. Guarnieri, On the Connection between Quantization of Nonintegrable Systems and Statistical Theory of Spectra, Lettere al Nuovo Cimento 28
1980
Earlier work this paper cites.
H. Fujisaka, Statistical dynamics generated by fluctuations of local Lyapunov exponents, Prog. Theor. Phys. 70
1983
Earlier work this paper cites.
O. Bohigas, M. J. Giannoni, and C. Schmit, Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws, Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
H. Frahm and H. Mikeska, On the dynamics of a quantum system which is classically chaotic, Zeitschrift für Physik B Condensed Matter 60
1985
Earlier work this paper cites.

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2019

Lyapunov growth in quantum spin chains

Craps, Ben, De Clerck, Marine, Janssens, Djunes et al.

Understand

The Ising spin chain with longitudinal and transverse magnetic fields is often used in studies of quantum chaos, displaying both chaotic and integrable regions in its parameter space.

However, even at a strongly chaotic point this model does not exhibit Lyapunov growth of the commutator squared of spin operators, as this observable saturates before exponential growth can manifest itself (even in situations where a spatial suppression factor makes the initial commutator small).
We extend this model from the spin 1/2 Ising model to higher spins, demonstrate numerically that a window of exponential growth opens up for sufficiently large spin, and extract a quantity which corresponds to a notion of a Lyapunov exponent.
In the classical infinite-spin limit, we identify and compute the appropriate classical analogue of the commutator squared, and show that the corresponding exponent agrees with the infinite-spin limit extracted from the quantum spin chain.

Built on

A. Schuckert and M. Knap, Many-body chaos near a thermal phase transition, SciPost Phys. 7
Original
1905
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, JETP 28
1969
Earlier work this paper cites.
M. V. Berry, and M. Tabor, Level clustering in the regular spectrum, Proc. Roy. Soc. A 356
1977
Earlier work this paper cites.
G. Casati, F. Valz-Gris, and I. Guarnieri, On the Connection between Quantization of Nonintegrable Systems and Statistical Theory of Spectra, Lettere al Nuovo Cimento 28
1980
Earlier work this paper cites.
H. Fujisaka, Statistical dynamics generated by fluctuations of local Lyapunov exponents, Prog. Theor. Phys. 70
1983
Earlier work this paper cites.
O. Bohigas, M. J. Giannoni, and C. Schmit, Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws, Phys. Rev. Lett. 52
1984
Earlier work this paper cites.
H. Frahm and H. Mikeska, On the dynamics of a quantum system which is classically chaotic, Zeitschrift für Physik B Condensed Matter 60
1985
Earlier work this paper cites.

Similar

R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, Characterisation of intermittency in chaotic systems, J. Phys. A: Math. Gen. 18
1985
Cited alongside, same era.
J. Madore, The fuzzy sphere, Classical and Quantum Gravity 9
1992
Cited alongside, same era.
M. C. Bañuls, J. I. Cirac, and M. B. Hastings, Strong and weak thermalization of infinite nonintegrable quantum systems, Phys. Rev. Lett. 106
2011
Cited alongside, same era.
S. Sachdev, Quantum Phase Transitions , 2nd ed. (Cambridge University Press, 2011)
2011
Cited alongside, same era.
Arseni Goussev, R. A. Jalabert, H. M. Pastawski, and D. Wisniacki, Loschmidt echo, Scholarpedia 7
2012
Cited alongside, same era.
A. Kitaev, Hidden correlations in the hawking radiation and thermal noise, talk given at Fundamental Physics Prize Symposium, Nov. 10, 2014