Project A06: Representation of quantum correlations in complex systems

Results

In the second funding phase we aimed to delve deeper into the intricate realm of quantum many-body systems far from equilibrium, building on the insights gained in the initial period. These systems, exemplified by optical and atomic clocks, as well as emerging NISQ devices, posed complex challenges. The project’s core objectives revolved around understanding these systems from various angles, integrating known methods to explore new frontiers.

One objective involved pioneering a noncommutative extension of the cumulant expansion, enabling systematic corrections to mean-field theory. Here waveguide QED was the focus of intensive investigations. The central result during the second funding period was an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles for chiral waveguide QED.

Another goal centered on developing classical simulation methods for complex quantum many-body systems, especially in the presence of defects and disorder. Advanced tensor network techniques took the spotlight, addressing gaps left by previous methods, notably in variational approaches. It was demonstrated, using novel tensor network methods, that many body disordered systems states feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. Thus these systems neither  equilibrate nor thermalise, in contrast to previous expectations from the literature.

In summary, A06 completely and comprehensively achieved all of the proposed objectives. It will be concluded at the end of the second funding period in 2024.