Curator's Take
This article introduces a fundamentally new approach to one of quantum simulation's biggest challenges: efficiently handling strongly correlated quantum systems that span multiple energy scales, from quantum chemistry molecules to condensed matter systems. The "nonadiabatic renormalization group" method cleverly suppresses rather than eliminates high-energy components, creating a sophisticated nested tensor network structure that could capture quantum correlations missed by traditional approaches like matrix product states. This mathematical innovation addresses a critical bottleneck in quantum simulation, where existing methods often struggle with systems where fast and slow dynamics are strongly coupled, potentially opening new pathways for simulating complex materials and chemical reactions that are currently beyond reach.
— Mark Eatherly
Summary
Complex quantum systems are often multiscale in nature with strong interactions between different scales. We present a novel idea: iteratively suppressing, rather than tracing out, the fast, high-energy degrees of freedom in strongly correlated quantum systems with multiple energy scales in a non-perturbative way, termed nonadiabatic renormalization group. This leads to a quantum geometric structure of a nested fiber bundle, in which each fiber of a layer is itself a fiber bundle of the next layer. The nonadiabatic renormalization group brings a new type of tensor network states that shares physical legs among ''sites'' and encodes quantum entanglement beyond conventional matrix product states. We demonstrate how to apply the nonadiabatic renormalization group to different types of problems, including an interacting boson model and ab initio quantum chemistry with interacting electrons.