Quantum information dynamics in multipartite integrable systems

¹ Delta Institute for Theoretical Physics, University of Amsterdam - Science Park 904, 1098 XH Amsterdam, The Netherlands
² International School for Advanced Studies (SISSA) and INFN - Via Bonomea 265, I-34136, Trieste, Italy
³ International Centre for Theoretical Physics (ICTP) - I-34151, Trieste, Italy

Received: 14 April 2019
Accepted: 18 June 2019

Abstract

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the Rényi mutual information with Rényi index . We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.