Monte Carlo Studies of Quantum Critical Metals

TL;DR

This paper reviews recent quantum Monte Carlo simulation progress on metallic quantum critical points, shedding light on non-Fermi liquid behavior, superconductivity, and transport phenomena in strongly correlated materials.

Contribution

It provides a comprehensive overview of QMC studies on metallic quantum criticality, highlighting new insights into spin density wave and Ising nematic critical points.

Findings

QMC simulations reveal non-Fermi liquid behavior near criticality

Results suggest connections between quantum criticality and high-temperature superconductivity

Progress in understanding transport properties at quantum critical points

Abstract

Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this article, we review the status of the understanding of metallic quantum criticality, and the recent progress made by QMC simulations. We focus on the cases of spin density wave and Ising nematic criticality. We describe the results obtained so far, and their implications for superconductivity, non-Fermi liquid behavior, and transport in the vicinity of metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.