Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case
arXiv:2301.02326 · doi:10.21468/SciPostPhysCore.7.1.005
Abstract
The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of \emph{branch-point twist fields}, the starting point for computing Rényi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of Rényi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.
53 pages, 2 figures
References in corpus (18)
- Entanglement negativity in quantum field theory
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Quantum Noise as an Entanglement Meter
- What is an integrable quench?
- Correlation functions and transport coefficients in generalised hydrodynamics
- Twist operators in higher dimensions
- Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
- On the theory of quantum quenches in near-critical systems
- Bi-partite entanglement entropy in massive two-dimensional quantum field theory
- Ballistic macroscopic fluctuation theory
- Quantum quenches with integrable pre-quench dynamics
- Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
- Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
- Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
- Hydrodynamic gauge fixing and higher order hydrodynamic expansion
- Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
- The hydrodynamic theory of dynamical correlation functions in the XX chain
- Interplay between transport and quantum coherences in free fermionic systems
Cited by in corpus (5)
- Generalized hydrodynamics: a perspective
- Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
- Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
- Full counting statistics after quantum quenches as hydrodynamic fluctuations
- Time Evolution of the Symmetry Resolved Entanglement Entropy after a Mass Quench