Power-law out of time order correlation functions in the SYK model

By Dmitry Bagrets, A. Altland, Alex Kamenev. 2017

212 citations recorded by the source corpus.

We evaluate the finite temperature partition sum and correlation functions of the Sachdev–Ye–Kitaev (SYK) model. Starting from a recently proposed mapping of the SYK model onto Liouville quantum mechanics, we obtain our results by exact integration over conformal Goldstone modes reparameterizing physical time. Perhaps, the least expected result of our analysis is that at time scales proportional to the number of particles the out of time order correlation function crosses over from a regime of exponential decay to a universal t−6 power-law behavior.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9e5687a487158e15957d6ca63d625ce5a626da21

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. D. Stanford
2. Phil Saad
3. Zhenbin Yang
4. E. Witten
5. S. Shenker
6. Alexei Y. Kitaev
7. G. Turiaci
8. J. Maldacena

In Condensed Matter Physics

1. E. Witten
2. D. Stanford
3. Alexei Y. Kitaev
4. G. Turiaci
5. H. Verlinde
6. Xiao-Liang Qi
7. S. J. Suh
8. Yingfei Gu

In Statistical and Nonlinear Physics

1. D. Stanford
2. Phil Saad
3. Zhenbin Yang
4. S. Shenker
5. G. Turiaci
6. E. Witten
7. Tom Mertens
8. J. Maldacena

Citations in the corpus

• Solving the Schwarzian via the conformal bootstrap (2017, methodology): “3) we can deduce a power-law decay as ∼ t−6 consistent with the results of [21].”
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual (2017, background): “Remarkably, this expression is valid even for βJ & N , when the fluctuations of the soft mode are strong [25, 27, 28].”
• The Schwarzian theory — origins (2018, methodology): “This leftover gauge symmetry is explicitly distilled in correlators in [34, 35].”
• Eternal traversable wormhole (2018, background): “36) was already shown to describe correctly the TFD (for η = 0) [30, 31, 32].”
• The quantum gravity dynamics of near extremal black holes (2018, methodology): “This problem was considered before in [4, 5, 6, 7, 8] from various points of view.”
• JT gravity as a matrix integral (2019, methodology): “The resulting path integral is the partition function of the Schwarzian theory, which has been computed by several different methods [20, 21, 22, 23, 24, 25] and it leads to the expression2”
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity (2019, background): “In JT gravity, these effects are captured by the coupling of the matter to the boundary [20, 24, 25, 23, 43].”
• JT gravity and the ensembles of random matrix theory (2019, methodology): “The contribution of a particular topology to the path (1)This has included many different derivations of the exact path integral [12, 13, 14, 15, 16, 17, 18, 19, 20], studies of the Hilbert space structure [21, 18, 22, 23], correlation functions [24, 25, 26], the physical symmetry charges [27], and ”
• Notes on the complex Sachdev-Ye-Kitaev model (2019, background): “The density of states (DOS) and the partition function for the pure Schwarzian model are as follows [33–36], where the energy E and the temperature β−1 are measured in units of (αSN) −1:”
• Statistical mechanics of a two-dimensional black hole (2018, methodology): “This seems to be the simplest and most robust interpretation of the density of states, which is implicit in [11, 12].”
• A semiclassical ramp in SYK and in gravity (2018, background): “(5)For related work on correlation functions see [26, 27].”