A Sport and a Pastime: Model Design and Computation in Quantum Many-Body Systems

TL;DR

This paper reviews recent advances in model design and computational methods for various quantum many-body systems, highlighting how tailored models and algorithms driven by experimental progress lead to new insights and phases.

Contribution

It introduces novel models and computational approaches inspired by experimental developments in quantum many-body physics.

Findings

Identification of new insulating phases in flat-band Moiré lattice models

Discovery of fluctuation-induced superconductivity in SYK models

Insights into quantum critical metals beyond traditional frameworks

Abstract

We summarize the recent developments in the model design and computation for a few representative quantum many-body systems, encompassing quantum critical metals beyond the Hertz-Millis-Moriya framework with pseudogap and superconductivity, SYK non-Fermi-liquid with self-tuned quantum criticality and fluctuation induced superconductivity, and the flat-band quantum Moir\'e lattice models in continuum where the interplay of quantum geometry of flat-band wave function and the long-range Coulomb interactions gives rise to novel insulating phases at integer fillings and superconductivity away from them. Although the narrative choreography seems simple, we show how important the appropriate model design and their tailor-made algorithmic developments -- in other words, the scientific imagination inspired by the corresponding fast experimental developments in the aforementioned systems -- compel us to invent and discover new knowledge and insights in the sport and pastime of quantum many-body research.