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

We apply the theory of Quantum Generalized Hydrodynamics (QGHD) introduced in [Phys. Rev. Lett. 124, 140603 (2020)] to derive asymptotically exact results for density fluctuations and entanglement entropy a one-dimensional trapped Bose gas Tonks-Girardeau (TG) or hard-core limit, after trap quench from double well single well. On analytical side, quadratic nature QGHD is complemented with emerging conformal invariance at TG point fix universal part those quantities. Moreover, well-known mapping bosons free fermions, allows use generalized form Fisher-Hartwig conjecture non-trivial spacetime dependence ultraviolet cutoff entropy. The also more accurate on numerical where higher number particles as compared interacting case can be simulated. agreement between predictions extremely good. For fluctuations, however, one has average out large Friedel oscillations present numerics recover such agreement.