Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model
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 bul...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)072 |
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| _version_ | 1832595073425997824 |
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| author | Pratik Nandy |
| author_facet | Pratik Nandy |
| author_sort | Pratik Nandy |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c89db6ced8a644359ee661c58bc87270 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-c89db6ced8a644359ee661c58bc872702025-01-19T12:07:29ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025112010.1007/JHEP01(2025)072Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK modelPratik Nandy0Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto UniversityAbstract 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.https://doi.org/10.1007/JHEP01(2025)072Matrix ModelsRandom SystemsHolography and Condensed Matter Physics (AdS/CMT) |
| spellingShingle | Pratik Nandy Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model Journal of High Energy Physics Matrix Models Random Systems Holography and Condensed Matter Physics (AdS/CMT) |
| title | Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model |
| title_full | Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model |
| title_fullStr | Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model |
| title_full_unstemmed | Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model |
| title_short | Tridiagonal Hamiltonians modeling the density of states of the double-scaled SYK model |
| title_sort | tridiagonal hamiltonians modeling the density of states of the double scaled syk model |
| topic | Matrix Models Random Systems Holography and Condensed Matter Physics (AdS/CMT) |
| url | https://doi.org/10.1007/JHEP01(2025)072 |
| work_keys_str_mv | AT pratiknandy tridiagonalhamiltoniansmodelingthedensityofstatesofthedoublescaledsykmodel |