Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach

TL;DR

This paper introduces a quantum Monte Carlo method that identifies the most significant correlations in many-body quantum systems, aiding the discovery of unknown order parameters without prior assumptions.

Contribution

It presents a novel approach using the correlation density matrix to detect dominant correlations in large quantum systems without prior knowledge.

Findings

Successfully applied to quantum Ising models and bilayer Heisenberg antiferromagnet

Able to identify phase transitions and order parameters systematically

Operates efficiently on large systems accessible to quantum Monte Carlo

Abstract

We present a quantum Monte Carlo-based approach to detect and compute the most dominant correlations for many-body systems without prior knowledge. It is based on the measurement and analysis of the correlation density matrix between two (small) subsystems embedded in the full (large) sample. In order to benchmark this procedure, we investigate zero-temperature quantum phase transitions in one- and two-dimensional quantum Ising model as well as the two-dimensional bilayer Heisenberg antiferromagnet. The method paves the way for a systematic identification of unknown or exotic order parameters in unexplored phases on large systems accessible to quantum Monte Carlo methods.