# Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques

## TL;DR

This review discusses recent advances in numerical methods, especially quantum Monte Carlo techniques, that have enabled the study of fermionic quantum criticality in complex condensed matter systems, providing new insights and potential experimental guidance.

## Contribution

It highlights novel model designs and algorithm improvements that allow unbiased large-scale simulations near quantum critical points, advancing understanding of fermionic quantum critical phenomena.

## Key findings

- Development of improved Monte Carlo algorithms for fermionic systems
- Large-scale numerical simulations revealing properties of quantum critical points
- Potential experimental implications for superconductors and cold atom systems

## Abstract

This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications and partially awaked by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems belong to the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc., where signatures of fermionic quantum criticality exist.