Work

Dynamical α -Rényi Entropies of Local Hamiltonians Grow at Most Linearly in Time

Year: 2025

Type: article

Abstract: We consider a generic one-dimensional spin system of length L , arbitrarily large, with strictly local interactions, for example, nearest neighbor, and prove that the dynamical α -Rényi entropies, 0 < α ≤ 1 , of an initial product state grow at most linearly in time. This result arises from a general relation among dynamical α -Rényi entropies and Lieb-Robinson bounds. We extend our bound on the dynamical generation of entropy to systems with exponential decay of interactions, for values of α close enough to 1, and, moreover, to initial pure states with low entanglement, of the order of log L , that are typically represented by critical states. We establish that low entanglement states have an efficient matrix product state representation that persists at least up to times of the order of log L . The main technical tools are the Lieb-Robinson bounds, to locally approximate the dynamics of the spin chain, a strict upper bound of Audenaert on α -Rényi entropies, and a bound on their concavity. Such a bound, that we provide in an appendix, can be of independent interest.

Source: Physical Review X

DOI: 10.1103/ycdh-z8zf

Authors: Daniele Toniolo, Sougato Bose

Institution: University College London

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $4,200

Funder: UK Research and Innovation