Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
arXiv:2410.07847 · doi:10.1007/JHEP01(2025)072
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 -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.
v2: rearranged texts and some sections; typos corrected; references added; to appear in JHEP
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Cited by in corpus (8)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Quantum complexity in gravity, quantum field theory, and quantum information science
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- Krylov space approach to Singular Value Decomposition in non-Hermitian systems
- Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
- Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
- Universal Time Evolution of Holographic and Quantum Complexity
- York time in JT gravity