Sprecher
Beschreibung
Information-theoretic quantities, such as Rényi entropies, exhibit remarkable universality in their late-time behavior across a wide range of chaotic quantum many-body systems. Understanding how these common features arise from vastly different microscopic dynamics remains an important challenge. In this talk, I will show this mechanism for a class of one-dimensional Brownian models with random, time-dependent Hamiltonians and a variety of microscopic couplings. In these models, the real-time Lorentzian evolution of the n-th Rényi entropy can be mapped onto an imaginary time Euclidean evolution of an effective Hamiltonian acting on 2n copies of the system. In the absence of symmetries, the ground states of this effective Hamiltonian resemble ferromagnets, hence its low-energy excitations are gapped domain walls between these ferromagnetic ground states. I will demonstrate how the membrane picture of entanglement growth naturally emerges from the physics of these domain-wall excitations, and show that the membrane tension is determined by their dispersion relation. While this prescription works straightforwardly for the computation of the membrane tension for the second Rényi entropy, there are subtleties that arise for higher Rényi entropies, which I will discuss. In all, this framework provides a universal understanding of entanglement dynamics in one dimension in terms of gapped low-lying modes, with potential extensions to non-random systems governed by time-independent Hamiltonians. Finally, I will discuss the fate of this picture in the presence of measurements, symmetries, and in higher-dimensional settings.
