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

Fuente: arXiv
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Autor principal: Nandy, Pratik
Formato: Preprint
Publicado: 2024
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author Nandy, Pratik
author_facet Nandy, Pratik
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_07847
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
Nandy, Pratik
High Energy Physics - Theory
Quantum Physics
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.
title Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
topic High Energy Physics - Theory
Quantum Physics
url https://arxiv.org/abs/2410.07847