Signatures of conformal symmetry in the dynamics of quantum gases: A cyclic quantum state and entanglement entropy

Year: 2024

Authors: Maki J., Zhou F.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Univ British Columbia, Dept Phys & Astron, 6224 Agr Rd, Vancouver, BC V6T 1Z1, Canada.

Abstract: Conformal symmetry heavily constrains the dynamics of nonrelativistic quantum gases tuned to a nearby quantum critical point. One important consequence of this symmetry is that entropy production can be absent in far-away-from-equilibrium dynamics of strongly interacting three-dimensional (3D) and one-dimensional (1D) quantum gases placed inside an adjustable harmonic trapping potential. This can lead to an oscillatory fully revivable many-body dynamic state, which is reflected in many physical observables. In this article we further investigate the consequences of conformal symmetry on (a) the zero-temperature autocorrelation function, (b) the Wigner distribution function, and (c) the von Neumann entanglement entropy. A direct calculation of these quantities for generic strongly interacting systems is usually extremely difficult. However, we have derived the general structures of these functions in the nonequilibrium dynamics when their dynamics are constrained by conformal symmetry. We obtain our results for (a) by utilizing an operator-state correspondence which connects the imaginary time evolution of primary operators to different initial states of harmonically trapped gases, while the dynamics of the functions in (b) and (c) are derived from conformal invariant density matrices.

Journal/Review: PHYSICAL REVIEW A

Volume: 110 (2)      Pages from: 23312-1  to: 23312-11

More Information: The authors would like to thank R. Hulet and S. Zhang for useful discussions. This project was partially supported by the NSERC (Canada) Discovery Grant under Grant No. RGPIN-2020-07070 and by the Provincia Autonoma di Trento.
KeyWords: Invariance; Scale
DOI: 10.1103/PhysRevA.110.023312

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