Dynamical Geometry of the Haldane Model under a Quantum Quench
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929570902441984 |
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| author | Qiu, Liwei Lim, Lih-King Wan, Xin |
| author_facet | Qiu, Liwei Lim, Lih-King Wan, Xin |
| contents | We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for non-equilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the pre-quench equilibrium state relaxes to the post-quench equilibrium state in an oscillatory fashion, whose amplitude decay as $t^{1/2}$. In the process, however, the characteristic winding vector of the non-equilibrium system can evolve to regimes that are not reachable with equilibrium states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Geometry of the Haldane Model under a Quantum Quench Qiu, Liwei Lim, Lih-King Wan, Xin Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Gases We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for non-equilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the pre-quench equilibrium state relaxes to the post-quench equilibrium state in an oscillatory fashion, whose amplitude decay as $t^{1/2}$. In the process, however, the characteristic winding vector of the non-equilibrium system can evolve to regimes that are not reachable with equilibrium states. |
| title | Dynamical Geometry of the Haldane Model under a Quantum Quench |
| topic | Mesoscale and Nanoscale Physics Other Condensed Matter Quantum Gases |
| url | https://arxiv.org/abs/2405.12470 |