In this talk, 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 and emergent gauge-field coupled with matter field 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.

References:
1. TOPICAL REVIEW, J. Phys.: Condens. Matter 31, 463001 (2019)
2. PNAS August 20, 2019 116 (34) 16760-16767
3. Phys. Rev. X 9, 021022 (2019)