Buividovich, PV 
ORCID: 0000-0002-9468-898X
(2022)
Quantum chaos in supersymmetric quantum mechanics: An exact diagonalization study.
PHYSICAL REVIEW D, 106 (4).
046001-.
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2205.09704.pdf - Author Accepted Manuscript Download (4MB) | Preview |
Abstract
We use exact diagonalization to study energy level statistics and out-of-time-order correlators (OTOCs) for the simplest supersymmetric extension H^S=H^B - I+x^1 - σ1+x^2 - σ3 of the bosonic Hamiltonian H^B=p^12+p^22+x^12x^22. For a long time, this bosonic Hamiltonian was considered one of the simplest systems which exhibit dynamical chaos both classically and quantum-mechanically. Its structure closely resembles that of spatially compactified pure Yang-Mills theory. Correspondingly, the structure of our supersymmetric Hamiltonian is similar to that of spatially compactified supersymmetric Yang-Mills theory, also known as the Banks-Fischler-Shenker-Susskind (BFSS) model. We present numerical evidence that a continuous energy spectrum of the supersymmetric model leads to monotonous growth of OTOCs down to the lowest temperatures, a property that is also expected for the BFSS model from holographic duality. We find that this growth is saturated by low-energy eigenstates with effectively one-dimensional wave functions and a completely nonchaotic energy level distribution. We observe a sharp boundary separating these low-energy states from the bulk of chaotic high-energy states. Our data suggest, although with limited confidence, that at low temperatures the OTOC growth might be exponential over a finite range of time, with the corresponding Lyapunov exponent scaling linearly with temperature. In contrast, the gapped low-energy spectrum of the bosonic Hamiltonian leads to oscillating OTOCs at low temperatures without any signatures of exponential growth. We also find that the OTOCs for the bosonic Hamiltonian are never sufficiently close to the classical Lyapunov distance. On the other hand, the OTOCs for the supersymmetric system agree with the classical limit reasonably well over a finite range of temperatures and evolution times.
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 23 Aug 2022 13:25 |
| Last Modified: | 15 Mar 2024 16:36 |
| DOI: | 10.1103/PhysRevD.106.046001 |
| Open Access URL: | https://doi.org/10.48550/arXiv.2205.09704 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3162087 |
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