Onset of random matrix behavior in scrambling systems
By Hrant Gharibyan, Masanori Hanada, S. Shenker, Masaki Tezuka. Journal of High Energy Physics, 2018
200 citations recorded by the source corpus.
A bstractThe fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We call this time tramp. The purpose of this paper is to study this scale in many-body quantum systems that display strong chaos, sometimes called scrambling systems. We focus on randomly coupled qubit systems, both local and k-local (all-to-all interactions) and the Sachdev-Ye-Kitaev (SYK) model. Using numerical results, analytic estimates for random quantum circuits, and a heuristic analysis of Hamiltonian systems we find the following results. For geometrically local systems with a conservation law we find tramp is determined by the diffusion time across the system, order N2 for a 1D chain of N qubits. This is analogous to the behavior found for local one-body chaotic systems. For a k-local system like SYK the time is order log N but with a different prefactor and a different mechanism than the scrambling time. In the absence of any conservation laws, as in a generic random quantum circuit, we find tramp ∼ log N, independent of connectivity.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/514e068cb1ceefb7f22661aeef7d6291154fe261
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
In Condensed Matter Physics
In Statistical and Nonlinear Physics
- Phil Saad
- D. Stanford
- S. Shenker
- M. Berkooz
- Genís Torrents
- Mikhail Isachenkov
- Vladimir Narovlansky
- Jordan S. Cotler
Citations in the corpus
- Towards a full solution of the large N double-scaled SYK model (2018, background): “The relation of SYK to random matrix theory was discussed in [19, 20].”
- JT gravity as a matrix integral (2019, background): “These features include the overall normalization of the Hamiltonian, as well as other low-order moments [20, 116, 117].”
- A semiclassical ramp in SYK and in gravity (2018, background): “This is the “ramp” or Thouless time (defined for example in [37] ) of the SYK model.”