Quantum generalized hydrodynamics of the Tonks–Girardeau gas: density fluctuations and entanglement entropy
- 20 December 2021
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (2), 024003
- https://doi.org/10.1088/1751-8121/ac3d68
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.Keywords
Funding Information
- ANR (ANR-20-CE30-0017-02)
- Swiss National Science Foundation
- CNRS Emerging International Actions (QuDOD)
- ERC consolidator grant (771536 (NEMO))
This publication has 59 references indexed in Scilit:
- Entanglement entropy and conformal field theoryJournal of Physics A: Mathematical and Theoretical, 2009
- Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field TheoryPhysical Review Letters, 2005
- Entanglement entropy and quantum field theoryJournal of Statistical Mechanics: Theory and Experiment, 2004
- Calculation of reduced density matrices from correlation functionsJournal of Physics A: General Physics, 2003
- Low-energy properties of a one-dimensional system of interacting bosons with boundariesEurophysics Letters, 2002
- Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground StatePhysical Review B, 1963
- Relationship between Systems of Impenetrable Bosons and Fermions in One DimensionJournal of Mathematical Physics, 1960
- The Evaluation of the Collision MatrixPhysical Review B, 1950
- Theory of the Superfluidity of Helium IIPhysical Review B, 1941
- On the Quantum Correction For Thermodynamic EquilibriumPhysical Review B, 1932