Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model
Pratik Nandy
Abstract
A bstract 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.
Topics & Concepts
PhysicsTridiagonal matrixSykStatistical physicsMathematical physicsQuantum electrodynamicsParticle physicsQuantum mechanicsTheoretical physicsEigenvalues and eigenvectorsBiochemistrySignal transductionChemistryTyrosine kinaseQuantum chaos and dynamical systemsQuantum many-body systemsCold Atom Physics and Bose-Einstein Condensates