Redundancies in Nambu-Goldstone Bosons
Haruki Watanabe, Hitoshi Murayama
TL;DR
This paper introduces a criterion to identify when Nambu-Goldstone bosons are redundant, explaining phenomena like phonons in crystals and superfluids, and clarifying the nature of Tkachenko modes in vortex lattices.
Contribution
It provides a simple criterion to determine redundancy of NGBs, resolving longstanding puzzles about gapless excitations in various condensed matter systems.
Findings
Phonons in crystals for broken translations are not redundant.
NGB for broken Galilean symmetry in superfluids is redundant with phonons.
Tkachenko mode in vortex lattices is identified as a Bogoliubov mode, showing redundancy.
Abstract
We propose a simple criterion to identify when Nambu-Goldstone bosons (NGBs) for different symmetries are redundant. It solves an old mystery why crystals have phonons for spontaneously broken translations but no gapless excitations for equally spontaneously broken rotations. Similarly for a superfluid, the NGB for spontaneously broken Galilean symmetry is redundant with phonons. The most nontrivial example is Tkachenko mode for a vortex lattice in a superfluid, where phonons are redundant to the Tkachenko mode which is identified as the Boboliubov mode.
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