Entanglement asymmetry in periodically driven quantum systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913931180638208 |
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| author | Banerjee, Tista Das, Suchetan Sengupta, K. |
| author_facet | Banerjee, Tista Das, Suchetan Sengupta, K. |
| contents | We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, $ΔS$, as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of $ΔS$ for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for $m$ cycles of a periodic drive with time period $T$, $ΔS \sim \ln mT$ [$\ln (\ln mT)$] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, $ΔS$ displays small amplitude oscillations around it's initial value as a function of $mT$. We provide a phase diagram for the behavior of $ΔS$ for such driven CFTs as a function of the drive frequency and amplitude. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_03654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement asymmetry in periodically driven quantum systems Banerjee, Tista Das, Suchetan Sengupta, K. Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, $ΔS$, as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of $ΔS$ for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for $m$ cycles of a periodic drive with time period $T$, $ΔS \sim \ln mT$ [$\ln (\ln mT)$] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, $ΔS$ displays small amplitude oscillations around it's initial value as a function of $mT$. We provide a phase diagram for the behavior of $ΔS$ for such driven CFTs as a function of the drive frequency and amplitude. |
| title | Entanglement asymmetry in periodically driven quantum systems |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.03654 |