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Open Quantum Systems Decoherence Quantum Simulation

Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model

arXiv
Authors: Pratik Nandy

Year

2024

Paper ID

38277

Status

Preprint

Abstract Read

~2 min

Abstract Words

91

Citations

N/A

Abstract

By analyzing the global density of states (DOS) in the Double-Scaled Sachdev-Ye-Kitaev (DSSYK) model, we construct a finite-dimensional Hamiltonian that replicates this DOS. We then tridiagonalize the Hamiltonian to determine the mean Lanczos coefficients within the parameter range. The bulk Lanczos coefficients, especially the Lanczos descent can be analytically expressed as a particular q-deformation of the logarithm. Our numerical results are further corroborated by semi-analytical findings, a random matrix potential construction in the bulk, and the analytic results at the edge of the Lanczos spectra using the method of moments.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • By analyzing the global density of states (DOS) in the Double-Scaled Sachdev-Ye-Kitaev (DSSYK) model, we construct a finite-dimensional Hamiltonian that replicates this DOS.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2410.07847 [2] arXiv https://arxiv.org/abs/2410.07847 [3] Publisher https://arxiv.org/abs/2410.07847

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