Page Curve and Entanglement Dynamics in an Interacting Fermionic Chain

TL;DR

This paper studies the entanglement dynamics in an interacting fermionic chain, revealing a non-analyticity in the entanglement entropy that signifies a quantum phase transition, with the nature of this transition depending on interaction strength.

Contribution

It introduces a detailed analysis of Page curve behavior in an interacting fermionic system, extending previous free fermion results to include interactions and their effects on entanglement phase transitions.

Findings

Non-analyticity in min-entropy separates two quantum phases.

Weak to intermediate interactions show a finite critical time for non-analyticity.

Strong interactions lead to instantaneous non-analyticity in entanglement dynamics.

Abstract

Generic non-equilibrium many-body systems display a linear growth of bipartite entanglement entropy in time, followed by a volume law saturation. In stark contrast, the Page curve dynamics of black hole physics shows that the entropy peaks at the Page time $t_{\text{Page}}$ and then decreases to zero. Here, we investigate such Page-like behavior of the von Neumann entropy in a model of strongly correlated spinless fermions in a typical system-environment setup, and characterize the properties of the Page curve dynamics in the presence of interactions using numerically exact matrix product states methods. The two phases of growth, namely the linear growth and the bending down, are shown to be separated by a non-analyticity in the min-entropy before $t_{\text{Page}}$, which separates two different quantum phases, realized as the respective ground states of the corresponding entanglement (or equivalently, modular) Hamiltonian. We confirm and generalize, by introducing interactions, the findings of \href{https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.224308}{Phys. Rev. B 109, 224308 (2024)} for a free spinless fermionic chain where the corresponding entanglement Hamiltonian undergoes a quantum phase transition at the point of non-analyticity. However, in the presence of interactions, a scaling analysis gives a non-zero critical time for the non-analyticity in the thermodynamic limit only for weak to intermediate interaction strengths, while the dynamics leading to the non-analyticity becomes \textit{instantaneous} for interactions large enough. We present a physical picture explaining these findings.