Order Parameter Discovery for Quantum Many-Body Systems

Quantum 10, 2217 (2026). https://doi.org/10.22331/q-2026-09-29-2217 Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without prior knowledge of order parameters remains a significant challenge. In this work, we introduce a method for constructing phase diagrams using the vector field of the reduced fidelity susceptibility (RFS), and demonstrate how information encoded in this vector field can be used to discover observables corresponding to order parameters. We apply our approach to well-established models: the Axial Next Nearest Neighbour Interaction (ANNNI) model, a cluster state model, and a chain of Rydberg atoms; and validate the discovered order parameters using eigendecomposition and finite-size scaling analysis, confirming the expected universality classes. Our results demonstrate that the RFS vector field offers a unified framework for phase characterization and order-parameter discovery that requires no prior knowledge of symmetry or transition type, while relying only on reduced density matrices of small subsystems.

Quantum phase transitions reveal deep insights into the behavior of many-body quantum systems, but identifying these transitions without prior knowledge of order parameters remains a significant challenge. In this work, we introduce a method for constructing phase diagrams using the vector field of the reduced fidelity susceptibility (RFS), and demonstrate how information encoded in this vector field can be used to discover observables corresponding to order parameters. We apply our approach to well-established models: the Axial Next Nearest Neighbour Interaction (ANNNI) model, a cluster state model, and a chain of Rydberg atoms; and validate the discovered order parameters using eigendecomposition and finite-size scaling analysis, confirming the expected universality classes. Our results demonstrate that the RFS vector field offers a unified framework for phase characterization and order-parameter discovery that requires no prior knowledge of symmetry or transition type, while relying only on reduced density matrices of small subsystems.

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