Entanglement dynamics from universal low-lying modes

TL;DR

This paper uncovers a universal low-energy mode structure underlying entanglement growth in chaotic many-body systems, linking it to gapped quasiparticle excitations and membrane tension dynamics.

Contribution

It demonstrates that entanglement dynamics can be understood through a universal gapped quasiparticle band in the Euclidean Hamiltonian, applicable across various chaotic systems.

Findings

Low-energy excitations are universal and gapped.

Membrane tension relates to quasiparticle dispersion.

Phase transitions in membrane tension occur for the third Renyi entropy.

Abstract

Information-theoretic quantities such as Renyi entropies show a remarkable universality in their late-time behaviour across a variety of chaotic many-body systems. Understanding how such common features emerge from very different microscopic dynamics remains an important challenge. In this work, we address this question in a class of Brownian models with random time-dependent Hamiltonians and a variety of different microscopic couplings. In any such model, the Lorentzian time-evolution of the $n$-th Renyi entropy can be mapped to evolution by a Euclidean Hamiltonian on 2$n$ copies of the system. We provide evidence that in systems with no symmetries, the low-energy excitations of the Euclidean Hamiltonian are universally given by a gapped quasiparticle-like band. The eigenstates in this band are plane waves of locally dressed domain walls between ferromagnetic ground states associated with two permutations in the symmetric group $S_n$. These excitations give rise to the membrane picture of entanglement growth, with the membrane tension determined by their dispersion relation. We establish this structure in a variety of cases using analytical perturbative methods and numerical variational techniques, and extract the associated dispersion relations and membrane tensions for the second and third Renyi entropies. For the third Renyi entropy, we argue that phase transitions in the membrane tension as a function of velocity are needed to ensure that physical constraints on the membrane tension are satisfied. Overall, this structure provides an understanding of entanglement dynamics in terms of a universal set of gapped low-lying modes, which may also apply to systems with time-independent Hamiltonians.