Spectral statistics and many-body quantum chaos with conserved charge
<p>We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor <em>K</em>(<em>t</em>) analytically for a minimal Floquet circuit model that has a <em>U</em>(1) symme...
| Main Authors: | , , , |
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| 格式: | Journal article |
| 出版: |
American Physical Society
2019
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| _version_ | 1826279784269742080 |
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| author | Friedman, A Chan, A Luca, A Chalker, J |
| author_facet | Friedman, A Chan, A Luca, A Chalker, J |
| author_sort | Friedman, A |
| collection | OXFORD |
| description | <p>We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor <em>K</em>(<em>t</em>) analytically for a minimal Floquet circuit model that has a <em>U</em>(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate <em>K</em>(<em>t</em>) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the “Thouless time” <em>t</em><sub>Th</sub> demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for <em>K</em>(<em>t</em>) at <em>t</em>≲<em>t</em><sub>Th</sub>. We also report numerical results for <em>K</em>(<em>t</em>) in a generic Floquet spin model, which are consistent with these analytic predictions.</p> |
| first_indexed | 2024-03-07T00:03:57Z |
| format | Journal article |
| id | oxford-uuid:76ea0fdb-a26d-4c08-a787-a6039b05074b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:03:57Z |
| publishDate | 2019 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:76ea0fdb-a26d-4c08-a787-a6039b05074b2022-03-26T20:19:31ZSpectral statistics and many-body quantum chaos with conserved chargeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:76ea0fdb-a26d-4c08-a787-a6039b05074bSymplectic Elements at OxfordAmerican Physical Society2019Friedman, AChan, ALuca, AChalker, J<p>We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor <em>K</em>(<em>t</em>) analytically for a minimal Floquet circuit model that has a <em>U</em>(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate <em>K</em>(<em>t</em>) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the “Thouless time” <em>t</em><sub>Th</sub> demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for <em>K</em>(<em>t</em>) at <em>t</em>≲<em>t</em><sub>Th</sub>. We also report numerical results for <em>K</em>(<em>t</em>) in a generic Floquet spin model, which are consistent with these analytic predictions.</p> |
| spellingShingle | Friedman, A Chan, A Luca, A Chalker, J Spectral statistics and many-body quantum chaos with conserved charge |
| title | Spectral statistics and many-body quantum chaos with conserved charge |
| title_full | Spectral statistics and many-body quantum chaos with conserved charge |
| title_fullStr | Spectral statistics and many-body quantum chaos with conserved charge |
| title_full_unstemmed | Spectral statistics and many-body quantum chaos with conserved charge |
| title_short | Spectral statistics and many-body quantum chaos with conserved charge |
| title_sort | spectral statistics and many body quantum chaos with conserved charge |
| work_keys_str_mv | AT friedmana spectralstatisticsandmanybodyquantumchaoswithconservedcharge AT chana spectralstatisticsandmanybodyquantumchaoswithconservedcharge AT lucaa spectralstatisticsandmanybodyquantumchaoswithconservedcharge AT chalkerj spectralstatisticsandmanybodyquantumchaoswithconservedcharge |