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Counting rule for Nambu-Goldstone modes in nonrelativistic systems
1Mathematical Physics Laboratory, RIKEN Nishina Center, Saitama 351-0198, Japan.
Physical Review Letters
|March 19, 2013
Summary
The study establishes a counting rule for Nambu-Goldstone modes in nonrelativistic systems. This rule relates the number of modes to the number of broken charges and the commutator of these charges.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Quantum Field Theory
Background:
- Nambu-Goldstone modes are fundamental excitations in systems with spontaneous symmetry breaking.
- Understanding their counting is crucial for characterizing phases of matter.
Purpose of the Study:
- To derive and validate a general counting rule for Nambu-Goldstone modes.
- To apply this rule in nonrelativistic systems at both zero and finite temperatures.
Main Methods:
- Utilized Mori's projection operator method.
- Analyzed systems with broken charges.
Main Results:
- Established a precise formula for the number of Nambu-Goldstone modes.
- The count equals the number of broken charges minus half the rank of the charge commutator's expectation value.
Conclusions:
- The derived counting rule is applicable to nonrelativistic systems.
- Provides a theoretical framework for identifying Nambu-Goldstone modes based on charge algebra.
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