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Related Experiment Video

Updated: May 11, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

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Published on: November 15, 2013

Redundancies in Nambu-Goldstone bosons.

Haruki Watanabe1, Hitoshi Murayama

  • 1Department of Physics, University of California, Berkeley, California 94720, USA. hwatanabe@berkeley.edu

Physical Review Letters
|May 21, 2013
PubMed
Summary

We introduce a criterion to identify redundant Nambu-Goldstone bosons. This explains why crystals lack gapless excitations for broken rotations and why superfluid phonons are redundant with Tkachenko modes.

Area of Science:

  • Condensed matter physics
  • Theoretical physics

Background:

  • Nambu-Goldstone bosons are associated with spontaneous symmetry breaking.
  • The existence of phonons in crystals and Tkachenko modes in superfluids has raised questions about redundancy.
  • Understanding these excitations is crucial for characterizing quantum phases of matter.

Purpose of the Study:

  • To propose a simple criterion for identifying redundant Nambu-Goldstone bosons.
  • To resolve the apparent paradox of gapless excitations in systems with spontaneously broken symmetries.
  • To clarify the relationship between phonons, Tkachenko modes, and Bogoliubov modes in superfluids.

Main Methods:

  • Theoretical analysis of symmetry breaking and associated excitations.
  • Application of the proposed criterion to crystalline solids and superfluids.

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  • Identification of specific modes, such as phonons and Tkachenko modes, within theoretical frameworks.

    • Main Results:

    • A criterion is proposed to determine when Nambu-Goldstone bosons are redundant.
    • The criterion explains the absence of gapless excitations for spontaneously broken rotations in crystals.
    • It is shown that phonons in superfluids are redundant with the Nambu-Goldstone mode associated with broken Galilean symmetry.
    • The Tkachenko mode in a superfluid vortex lattice is identified as redundant with phonons and equivalent to the Bogoliubov mode.

    Conclusions:

    • The proposed criterion offers a unified explanation for the presence or absence of gapless excitations in various physical systems.
    • It clarifies the nature of Tkachenko modes as Bogoliubov modes, resolving redundancy with phonons.
    • This work provides a fundamental insight into the characterization of collective excitations in condensed matter systems.