Quantitative Quantum Matter Analysis

Objective

The assumption that the plain vanilla single-band Hubbard model captures the relevant physics of the cuprate materials has been a key motivation for a host of numerical work and quantum simulation experiments. Recent numerical advances challenge this assumption and raise the pressing question: which minimal model can be used to understand quantum materials exhibiting unconventional superconductivity? However, extracting the relevant Hamiltonian of real materials is a formidable challenge and usually involves ab-initio methods that only approximately capture strong correlations. The goal of QuaQuaMA is to perform Hamiltonian reconstruction for materials by developing a novel approach where strong correlations take center stage: we will systematically compare observables from experiments on materials with quantum simulators and large-scale numerics, which directly take strong interactions into account. Building upon this year’s Nobel prize work, we will develop and use neural networks to simulate interacting quantum many-body systems. The number of simulations for different candidate Hamiltonians will be minimized through a highly efficient, machine learning based exploration of the vast parameter space. Our advanced numerical methods, in combination with quantum simulation experiments, will also enable the exploration of the phase diagrams of the determined effective Hamiltonians, employing novel observables to reveal the underlying physics. We will focus on three particularly interesting, related material classes with the ultimate goal to distill the essence of unconventional superconductivity: cuprates, infinite layer nickelates, and bilayer nickelates. The Hamiltonian reconstruction framework established in QuaQuaMA will be applicable far beyond these materials, for example to study effective Hamiltonians in the context of light-induced superconductivity, thus generating an enormous impact in the fields of strongly correlated electron systems and quantum simulat