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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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Published on: August 30, 2013

Order parameter for symmetry-protected phases in one dimension.

Jutho Haegeman¹, David Pérez-García, Ignacio Cirac

¹Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Wien, Austria.

Physical Review Letters

|September 26, 2012

Summary

We developed a new order parameter to identify symmetry-protected phases in one dimension. This tool, independent of specific states, accurately detects dimerized, Haldane, and gapless phases, with potential for cold atom experiments.

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Area of Science:

Condensed Matter Physics
Quantum Many-Body Systems
Topological Phases of Matter

Background:

Identifying and classifying symmetry-protected phases is crucial in one-dimensional quantum systems.
Conventional order parameters often depend on the specific ground state, limiting their universality.

Purpose of the Study:

To introduce a novel, state-independent order parameter for symmetry-protected phases in one dimension.
To demonstrate the efficacy of this order parameter in identifying distinct phases, including gapless ones.

Main Methods:

Development of a new order parameter based on stringlike operators and swaps.
Numerical simulations of the SO(3) invariant spin-1 bilinear-biquadratic model.
Verification of the order parameter's ability to distinguish between dimerized, Haldane, and gapless phases.

Main Results:

The proposed order parameter successfully identifies symmetry-protected phases without state dependence.
Distinct signatures were observed for dimerized, Haldane, and gapless phases.
The framework shows excellent performance for the SO(3) invariant spin-1 bilinear-biquadratic model.

Conclusions:

The novel order parameter provides a direct and universal method for classifying one-dimensional symmetry-protected phases.
The findings pave the way for experimental detection using cold atom systems.
This approach offers a powerful tool for exploring quantum phases of matter.