Computing quantum phase transitions

TL;DR

This paper reviews computational methods for quantum phase transitions, highlighting Monte Carlo techniques and their applications to various quantum systems, addressing the challenges in simulating these critical phenomena.

Contribution

It provides a comprehensive overview of classical and quantum Monte Carlo methods applied to quantum phase transitions, emphasizing recent computational strategies and examples.

Findings

Monte Carlo methods effectively simulate quantum phase transitions

Quantum-to-classical mapping aids classical Monte Carlo approaches

Direct quantum Monte Carlo methods tackle complex quantum systems

Abstract

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.