Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy
arXiv:2107.05655 · doi:10.1088/1751-8121/ac3d68
Abstract
We apply the theory of Quantum Generalized Hydrodynamics (QGHD) introduced in [Phys. Rev. Lett. 124, 140603 (2020)] 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.
arXiv comment16 pages, 2 figures (small updates/corrections)
References in corpus (47)
- Entanglement Entropy and Quantum Field Theory
- Entanglement entropy and conformal field theory
- Calculation of reduced density matrices from correlation functions
- Quantum Inverse Scattering Method and Correlation Functions
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Reduced density matrices and entanglement entropy in free lattice models
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
- Bosonizing one-dimensional cold atomic gases
- Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
- Nonlinear fluctuating hydrodynamics for anharmonic chains
- Generalized HydroDynamics on an Atom Chip
- Density-Matrix Spectra of Solvable Fermionic Systems
- Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases
- Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics
- Quantum Generalized Hydrodynamics
- Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
- Entanglement evolution and generalised hydrodynamics: noninteracting systems
- Random Matrix Theory and Entanglement in Quantum Spin Chains
- Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
- Observation of Dynamical Fermionization
- Density-matrix spectra for integrable models
- Universal corrections to scaling for block entanglement in spin-1/2 XX chains
- On the reduced density matrix for a chain of free electrons
- Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
- Entanglement evolution and generalised hydrodynamics: interacting integrable systems
- Density Matrices for a Chain of Oscillators
- Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
- Quantum ripples over a semi-classical shock
- Domain-wall melting in the spin- XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
- Locally quasi-stationary states in noninteracting spin chains
- Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
- Wigner function of noninteracting trapped fermions
- The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases
- One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
- Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
- Fermi distribution of semicalssical non-eqilibrium Fermi states
- Low-Energy Properties of a One-dimensional System of Interacting bosons with Boundaries
- Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas
- Split Fermi seas in one-dimensional Bose fluids
- One-particle density matrix of a trapped Lieb-Liniger anyonic gas
- Inhomogeneous Gaussian Free Field inside the interacting arctic curve
- General finite-size effects for zero-entropy states in one-dimensional quantum integrable models
- Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
- Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap
- Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel
- Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid