Lattice models and Monte Carlo solutions for quantum criticality

I will review recent developments in a priori and a posteriori numerical strategies in dealing with quantum many-body systems. Thanks to these philosophical and numerical advancements, novel paradigms in condensed matter and high energy physics such as non-Fermi-liquid, quantum criticality, emergent gauge-field coupled with matter field and SYK holographic quantum matter can be readily accessed with large-scale numerical simulations. These results in turn inspire further analytical and numerical progress towards the complete understanding of few important quantum many-body physics problems.