Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case

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 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.

Ballistic macroscopic fluctuation theory

“…The BMFT as formulated here can also be extended to describe ballistic large deviations more generally, such as under time evolution with long-wavelength, low-frequency variations of external fields and coupling parameters [105][106][107], and with initial conditions that already include long-range correlations such as those appearing after quantum quenches [95,108,109]. As suggested in [20], ballistic fluctuations are connected to objects called "twist fields", which have many interesting applications, including for the study of entanglement [110]; this is another area where the BMFT may offer new insight.…”

Boundary chaos: Exact entanglement dynamics

“…( 17). We introduce the folded gate W = U † ⊗ U T and V = W S (which is the folded version of the gate V = U P in the case of states) and use the same diagrammatic representation (18). The gate V is again unitary, which is diagrammatically depicted by Eq.…”

“…This linear growth has been observed in distinguished scenarios, including experimental setups with cold atoms [5], and has been explained by different mechanisms. In integrable systems, the linear growth can be traced back to propagating stable quasi particles [12][13][14][15][16][17][18]. But it has also been shown that the linear growth is ubiquitous even in the absence of stable quasi particle excitations [19][20][21][22][23][24][25][26][27][28][29][30].…”

Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

“…(2023) 073102 theoretical works about the FCS has been also motivated by the recent groundbreaking advances with cold atom experiments [35][36][37][38][39][40][41]. Shifting the attention to observables with support on a finite, but large, subsystem embedded in a thermodynamic system provides a further motivation for studying the FCS: indeed, it turned out to be strictly related to the entanglement entropy of the same subsystem [42][43][44][45][46][47][48][49][50][51][52][53][54] and so it provides indirect information about the latter. This interplay will be relevant in our work, too, especially for the connections between the FCS and the entanglement entropy in a given charge sector in the presence of a global symmetry.…”