Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

TL;DR

This paper reviews recent advances in sign-problem-free fermionic quantum Monte Carlo algorithms, highlighting their development, applications to complex quantum systems, and future research directions, enabling reliable simulations of large-scale, low-temperature quantum models.

Contribution

It introduces new sign-problem-free QMC algorithms using Majorana representation and hot-spot physics, expanding the toolkit for simulating complex quantum systems.

Findings

Development of sign-problem-free algorithms for fermionic systems

Successful application to models of high-temperature superconductors and frustrated magnets

Discussion of future directions for algorithm design

Abstract

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically-exact and intrinsically-unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion-sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously-broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progresses made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.