Systematic Derivation of Order Parameters through Reduced Density Matrices

TL;DR

This paper introduces a systematic approach using reduced density matrices to identify order parameters in quantum many-body systems, enabling discovery of unknown exotic orders directly from ground state wave functions.

Contribution

The method provides a direct, empirical-free way to derive order parameters, applicable to various models with exotic quantum orders.

Findings

Successfully applied to models with dimer, scalar chiral, and topological orders

Enables exploration of unknown quantum orders without prior empirical knowledge

Demonstrates both numerical and rigorous validation

Abstract

A systematic method for determining order parameters for quantum many-body systems on lattices is developed by utilizing reduced density matrices. This method allows one to extract the order parameter directly from the wave functions of the degenerate ground states without aid of empirical knowledge, and thus opens a way to explore unknown exotic orders. The applicability of this method is demonstrated numerically or rigorously in models which are considered to exhibit dimer, scalar chiral, and topological orders.