Buividovich, P 
ORCID: 0000-0002-9468-898X
(2023)
Quantum chaos in supersymmetric Yang-Mills-like model: equation of state, entanglement, and spectral form-factors.
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Abstract
We analyze in detail a sharp transition between the low-energy, low-dimensional eigenstates and the high-energy chaotic bulk of the spectrum for a simple supersymmetric quantum-mechanical model with Hamiltonian ĤS = ((Equation presented)21 + (Equation presented)22 + (Equation presented)12 (Equation presented)22) ⊗ I + (Equation presented)1 ⊗ σ1 + (Equation presented)2 ⊗ σ3, which mimics the structure of the Banks-Fischler-Susskind-Stanford (BFSS) matrix model, the spatially compactified N = 1 super-Yang-Mills theory. We conjecture that this transition might be similar to the transition between the D0-brane and M-theory regimes in the BFSS model, and find that it does not lead to irregularities in the thermodynamic equation of state. We demonstrate that real-time spectral form-factor for our supersymmetric model exhibits the “ramp” behavior typical for quantum chaos. We also analyze the entanglement entropy and the spectrum of the reduced density matrix of the eigenstates of ĤS, considering one of the bosonic degrees of freedom as a subsystem. The entanglement entropy of low-energy eigenstates appears to be practically energy-independent. Exactly at the onset of random-matrix-type level spacing fluctuations, this behavior rapidly changes into a steady growth of entanglement with energy. We demonstrate that the spectrum of the reduced density matrix also exhibits universal level-spacing fluctuations towards its higher end, even for the ground state of the supersymmetric model. Thus even the regularly spaced, non-chaotic eigenstates contain some information about semi-classical chaotic dynamics at high energies.
| Item Type: | Conference or Workshop Item (Unspecified) |
|---|---|
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 02 Oct 2023 14:58 |
| Last Modified: | 02 Oct 2023 14:58 |
| Open Access URL: | https://pos.sissa.it/430/246 |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3173312 |
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