Journal of Physics A: Mathematical and Theoretical PAPER Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy Paola Ruggiero6,1,4, Pasquale Calabrese2,3, Benjamin Doyon4 and Jérôme Dubail5 Published 20 December 2021 • © 2021 IOP Publishing Ltd Journal of Physics A: Mathematical and Theoretical, Volume 55, Number 2 Hydrodynamics of Low-Dimensional Quantum Systems Citation Paola Ruggiero et al 2022 J. Phys. A: Math. Theor. 55 024003 DownloadArticle PDF Figures References Open science 98 Total downloads 11 citation on Dimensions.Article has an altmetric score of 1 Turn on MathJax Get permission to re-use this article Share this article Share this content via email Share on Facebook (opens new window) Share on Twitter (opens new window) Share on Mendeley (opens new window) Article information Abstract We apply the theory of quantum generalized hydrodynamics (QGHD) introduced in (2020 Phys. Rev. Lett. 124 140603) to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks–Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher–Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.

Quantum generalized hydrodynamics of the Tonks-Girardeau gas: Density fluctuations and entanglement entropy / Ruggiero, P.; Calabrese, P.; Doyon, B.; Dubail, J.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:2(2021), pp. 1-21. [10.1088/1751-8121/ac3d68]

Quantum generalized hydrodynamics of the Tonks-Girardeau gas: Density fluctuations and entanglement entropy

Ruggiero, P.;Calabrese, P.;Doyon, B.;Dubail, J.
2021

Abstract

Journal of Physics A: Mathematical and Theoretical PAPER Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy Paola Ruggiero6,1,4, Pasquale Calabrese2,3, Benjamin Doyon4 and Jérôme Dubail5 Published 20 December 2021 • © 2021 IOP Publishing Ltd Journal of Physics A: Mathematical and Theoretical, Volume 55, Number 2 Hydrodynamics of Low-Dimensional Quantum Systems Citation Paola Ruggiero et al 2022 J. Phys. A: Math. Theor. 55 024003 DownloadArticle PDF Figures References Open science 98 Total downloads 11 citation on Dimensions.Article has an altmetric score of 1 Turn on MathJax Get permission to re-use this article Share this article Share this content via email Share on Facebook (opens new window) Share on Twitter (opens new window) Share on Mendeley (opens new window) Article information Abstract We apply the theory of quantum generalized hydrodynamics (QGHD) introduced in (2020 Phys. Rev. Lett. 124 140603) to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks–Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher–Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.
55
2
1
21
024003
https://arxiv.org/abs/2107.05655
Ruggiero, P.; Calabrese, P.; Doyon, B.; Dubail, J.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/128394
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