Constants of motion characterizing continuous symmetry-broken phases

Area of Science:

• Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• Continuous symmetry-breaking is fundamental to many quantum and classical systems.
• Understanding the emergent phases and their dynamics is crucial for theoretical advancements.
• Conserved charges play a key role in characterizing these phases.

Purpose of the Study:

• To present a novel theory for characterizing phases arising from continuous symmetry-breaking.
• To establish a method for determining the nature of privileged directions in ordered phases.
• To provide a numerical example of the theory using a relevant physical model.

Main Methods:

• Development of a theoretical framework for symmetry-breaking phases.
• Analysis of conserved charges derived from the order parameter.
• Numerical investigation using the two-dimensional limit of the vibron model.

Main Results:

• The theory successfully characterizes emergent phases due to continuous symmetry-breaking.
• Conserved charges are shown to be determined by the privileged direction.
• The method allows for the distinction between well-defined and fluctuating privileged directions.

Conclusions:

• The presented theory offers a robust method for analyzing symmetry-breaking phenomena.
• The expectation values of conserved charges are key indicators of phase properties.
• The vibron model serves as a valid numerical test case for the theory.