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

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.

Automated summary

In this study, the theory of quantum generalized hydrodynamics (QGHD) is applied to derive exact results for density fluctuations and entanglement entropy of a one-dimensional trapped Bose gas after a trap quench. The analytical calculations demonstrate the quadratic nature of QGHD and the emergence of conformal invariance at the Tonks-Girardeau (TG) point. The numerical simulations show excellent agreement with the analytical predictions, with a more accurate representation achieved due to the free nature of the TG gas.