Nonadiabatic Renormalization Group for Strongly Coupled Multiscale Quantum Systems

TL;DR

This paper introduces a nonadiabatic renormalization group method that iteratively suppresses high-energy degrees of freedom in multiscale quantum systems, revealing a quantum geometric structure and enabling new tensor network states.

Contribution

It proposes a novel non-perturbative renormalization approach for strongly coupled multiscale quantum systems, extending tensor network techniques.

Findings

Developed a quantum geometric fiber bundle structure.

Created a new tensor network state with shared physical legs.

Applied method to boson models and quantum chemistry.

Abstract

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.