Flow Equation Approach to Periodically Driven Quantum Systems
We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group–like flow equations are derived to produce the eff...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-05-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.9.021037 |
| _version_ | 1818989950504271872 |
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| author | Michael Vogl Pontus Laurell Aaron D. Barr Gregory A. Fiete |
| author_facet | Michael Vogl Pontus Laurell Aaron D. Barr Gregory A. Fiete |
| author_sort | Michael Vogl |
| collection | DOAJ |
| description | We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group–like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency—and drive strength—regimes that are usually inaccessible via high-frequency ω expansions in the parameter h/ω, where h is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy model and test an approximate version of it on both interacting and noninteracting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high-frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high-frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel nonequilibrium regimes and behaviors in driven quantum many-particle systems. |
| first_indexed | 2024-12-20T19:46:37Z |
| format | Article |
| id | doaj.art-fa04ef11e9ef44c284b57bb2c8028bcd |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-20T19:46:37Z |
| publishDate | 2019-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-fa04ef11e9ef44c284b57bb2c8028bcd2022-12-21T19:28:24ZengAmerican Physical SocietyPhysical Review X2160-33082019-05-019202103710.1103/PhysRevX.9.021037Flow Equation Approach to Periodically Driven Quantum SystemsMichael VoglPontus LaurellAaron D. BarrGregory A. FieteWe present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization-group–like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency—and drive strength—regimes that are usually inaccessible via high-frequency ω expansions in the parameter h/ω, where h is the upper limit for the strength of local interactions. We demonstrate exact properties of our approach on a simple toy model and test an approximate version of it on both interacting and noninteracting many-body Hamiltonians, where it offers an improvement over the more well-known Magnus expansion and other high-frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high-frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel nonequilibrium regimes and behaviors in driven quantum many-particle systems.http://doi.org/10.1103/PhysRevX.9.021037 |
| spellingShingle | Michael Vogl Pontus Laurell Aaron D. Barr Gregory A. Fiete Flow Equation Approach to Periodically Driven Quantum Systems Physical Review X |
| title | Flow Equation Approach to Periodically Driven Quantum Systems |
| title_full | Flow Equation Approach to Periodically Driven Quantum Systems |
| title_fullStr | Flow Equation Approach to Periodically Driven Quantum Systems |
| title_full_unstemmed | Flow Equation Approach to Periodically Driven Quantum Systems |
| title_short | Flow Equation Approach to Periodically Driven Quantum Systems |
| title_sort | flow equation approach to periodically driven quantum systems |
| url | http://doi.org/10.1103/PhysRevX.9.021037 |
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