TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.1.005
TI  - Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case
PY  - 2024/02/14
UR  - https://scipost.org/SciPostPhysCore.7.1.005
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 1
SP  - 005
A1  - del Vecchio del Vecchio, Giuseppe
AU  - Doyon, Benjamin
AU  - Ruggiero, Paola
AB  - 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 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.
ER  -

@Article{10.21468/SciPostPhysCore.7.1.005,
	title={{Entanglement Rényi entropies from ballistic fluctuation theory: The free fermionic case}},
	author={Giuseppe del Vecchio del Vecchio and Benjamin Doyon and Paola Ruggiero},
	journal={SciPost Phys. Core},
	volume={7},
	pages={005},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.1.005},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.1.005},
}