Order Parameter Discovery for Quantum Many-Body Systems

TL;DR

This paper introduces a new method to identify quantum phase transitions and order parameters in many-body systems using reduced fidelity susceptibility, applicable even when traditional order parameters are unknown.

Contribution

The authors develop a novel approach that constructs phase diagrams and discovers order parameters through an optimization framework based on RFS, demonstrated on multiple quantum models.

Findings

Successfully identifies order parameters in complex quantum models

Accurately characterizes quantum phase transitions with finite-size scaling

Provides a versatile tool for exploring quantum phases without conventional order parameters

Abstract

Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without well-defined order parameters remains a significant challenge. In this work, we introduce a novel approach to constructing phase diagrams using the vector field of the reduced fidelity susceptibility (RFS). This method maps quantum phases and formulates an optimization problem to discover observables corresponding to order parameters. We demonstrate the effectiveness of our approach by applying it to well-established models, including the Axial Next Nearest Neighbour Interaction (ANNNI) model, a cluster state model, and a chain of Rydberg atoms. By analyzing observable decompositions into eigen-projectors and finite-size scaling, our method successfully identifies order parameters and characterizes quantum phase transitions with high precision. Our results provide a powerful tool for exploring quantum phases in systems where conventional order parameters are not readily available.