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Updated: Sep 13, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

Zero Curvature Condition for Quantum Criticality.

Chaoming Song¹

¹University of Miami, Department of Physics, Coral Gables, Florida 33146, USA.

Physical Review Letters

|July 31, 2025

Summary

This summary is machine-generated.

We introduce a geometric approach to understand quantum phase transitions by analyzing operator competition. Quantum criticality emerges at zero-curvature points, indicating maximal commutativity and potential integrability.

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Area of Science:

Condensed matter physics
Quantum mechanics

Background:

Quantum criticality challenges conventional theories like the Landau paradigm.
The diversity of quantum orders hinders a unified framework for quantum phase transitions.

Purpose of the Study:

To propose a novel geometric framework for understanding quantum phase transitions.
To shift focus from microscopic order to operator competition.

Main Methods:

Developing a geometric approach based on the boundary geometry of operator expectation values.
Defining a quantum observable space to encode operator competition.

Main Results:

Quantum phase transitions are identified at zero-curvature points in the quantum observable space.
These points signify maximal commutativity between operators.

Conclusions:

The geometric approach offers a new perspective on quantum criticality.
Zero-curvature points suggest an underlying integrable structure at quantum critical points.