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J. Jiang and Z. Yang, Thermodynamics and Many Body Chaos for generalized large q SYK models
Original
1905
Earlier work this paper cites.
J. L. F. Barbón, E. Rabinovici, R. Shir, and R. Sinha, On The Evolution Of Operator Complexity Beyond Scrambling
Original
1907
Earlier work this paper cites.
A. Avdoshkin and A. Dymarsky, Euclidean operator growth and quantum chaos
Original
1911
Earlier work this paper cites.
T. Xu, T. Scaffidi, and X. Cao, Does scrambling equal chaos?
Original
1912
Earlier work this paper cites.
A. Dymarsky and A. Gorsky, Quantum chaos as delocalization in Krylov space
Original
1912
Earlier work this paper cites.
C. Choi, M. Mezei, and G. Sárosi, Exact four point function for large q q SYK from Regge theory
Original
1912
Earlier work this paper cites.
Gauthier-Villars, Paris, 1926
T. Carleman, Les fonctions quasi analytiques · 1926
Earlier work this paper cites.
J. B. French and S. S. M. Wong, Some random-matrix level and spacing distributions for fixed-particle-rank interactions
1971
Earlier work this paper cites.
S. Sachdev and J. Ye, Gapless spin-fluid ground state in a random quantum heisenberg magnet
1993
Earlier work this paper cites.
Lecture Notes in Physics Monographs. Springer Berlin Heidelberg, 1994
V. Viswanath and G. Müller, The Recursion Method: Application to Many Body Dynamics · 1994
Earlier work this paper cites.
E. Brézin and S. Hikami, Spectral form factor in a random matrix theory
1997
Earlier work this paper cites.
Y. D. Lensky, X.-L. Qi, and P. Zhang, Size of bulk fermions in the SYK model
Original
2002
Earlier work this paper cites.
J. M. Magan and J. Simon, On operator growth and emergent Poincaré symmetries
Original
2002
Earlier work this paper cites.
M. Berkooz, N. Brukner, V. Narovlansky, and A. Raz, The double scaled limit of Super–Symmetric SYK models
Original
2003
Earlier work this paper cites.
M. Berkooz, V. Narovlansky, and H. Raj, Complex Sachdev-Ye-Kitaev model in the double scaling limit
Original
2006
Earlier work this paper cites.
S.-K. Jian, B. Swingle, and Z.-Y. Xian, Complexity growth of operators in the SYK model and in JT gravity
Original
2008
Earlier work this paper cites.
K. Schmüdgen, Ten Lectures on the Moment Problem
Original
2008
Earlier work this paper cites.
E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, Operator complexity: a journey to the edge of Krylov space
Original
2009
Earlier work this paper cites.
L. F. Santos and M. Rigol, Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
Original
2010
Earlier work this paper cites.
Dover Books on Mathematics. Dover Publications, Reprint edition, 2011
T. Chihara, An Introduction to Orthogonal Polynomials · 2011
Earlier work this paper cites.
M. Khramtsov and E. Lanina, Spectral form factor in the double-scaled SYK model
Original
2011
Earlier work this paper cites.
X. Cao, A statistical mechanism for operator growth
Original
2012
Earlier work this paper cites.
N. Lashkari, D. Stanford, M. Hastings, T. Osborne, and P. Hayden, Towards the Fast Scrambling Conjecture
Original
2013
Earlier work this paper cites.
L. Erdős and D. Schröder, Phase transition in the density of states of quantum spin glasses
Original
2014
Earlier work this paper cites.
D. A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect
Original
2015
Earlier work this paper cites.
D. A. Roberts, D. Stanford, and L. Susskind, Localized shocks
Original
2015
Earlier work this paper cites.
Talk given at KITP
A. Kitaev, “A simple model of quantum holography (part 1) and (part 2).” https://online.kitp.ucsb.edu/online/joint98/kitaev/ , https://online.kitp.ucsb.edu/online/entangled15/kitaev2/ , 2015 · 2015
Earlier work this paper cites.
D. A. Roberts and B. Swingle, Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
Original
2016
Earlier work this paper cites.

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2022

Krylov complexity in large-$q$ and double-scaled SYK model

Bhattacharjee, Budhaditya, Nandy, Pratik, Pathak, Tanay

Understand

Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects.

The Krylov complexity naturally describes the "size" of the distribution, while the higher cumulants encode richer information.
We further consider the double-scaled limit of SYK$_q$ at infinite temperature, where $q \sim \sqrt{N}$.
In such a limit, we find that the scrambling time shrinks to zero, and the Lanczos coefficients diverge.