The time evolution of local information
Claudia Artiaco (KTH Stockholm)
During the time evolution of many-body systems entanglement spreads rapidly, limiting exact simulations to small-scale systems and small timescales. Quantum information tends, however, to flow towards larger scales without returning to local scales, such that its detailed large-scale structure does not directly affect local observables. This allows for the removal of large-scale quantum information in a way that preserves all local observables and gives access to large-scale and large-time quantum dynamics. To this end, in  we proposed a novel approach that uses the recently introduced information lattice to organize quantum information into different scales , allowing us to define local information and information currents which we employ to systematically discard long-range quantum correlations in a controlled way. Our approach relies on decomposing the system into subsystems up to a maximum scale and time evolving the subsystem density matrices by solving the subsystem von Neumann equations in parallel. Importantly, the information flow needs to be preserved during the discarding of large-scale information. To achieve this without the need to make assumptions about the microscopic details of the information current, we introduce a second scale at which information is discarded while using the state at the maximum scale to accurately obtain the information flow. The resulting algorithm, to which we refer to as local-information time evolution (LITE), is highly versatile and suitable for investigating many-body quantum dynamics in both closed and open quantum systems with diverse hydrodynamic behaviors.
In this talk, I will present results obtained via LITE for the energy transport in the mixed-field Ising model, where we accurately determine the power-law exponent and the energy diffusion constant . Furthermore, I will sketch how we used the LITE approach to reproduce and interpret the results found in a recent experiment with NV centers in diamonds . Finally, I will briefly mention how the information lattice can be employed to obtain insightful results about the spatial structure of entanglement in generic many-body quantum states .
 T. Klein Kvorning, L. Herviou, and J. H. Bardarson, Time-evolution of local information: Thermalization dynamics of local observables, SciPost Phys. 13, 080 (2022).
 C. Artiaco, C. Fleckenstein, D. Aceituno, T. Klein Kvorning, and J. H. Bardarson, Efficient Large-Scale Many- Body Quantum Dynamics via Local-Information Time Evolution, arXiv:2310:06036.
 K. Harkins et al., Nanoscale engineering and dynamical stabilization of mesoscopic spin textures, arXiv:2310:05635.
 C. Artiaco, T. Klein Kvorning, D. Aceituno, L. Herviou, and J. H. Bardarson, In preparation, 2024.