Condensed Matter Seminar : Fracton-elasticity duality for a Wigner crystal and the anti-Higgs mechanism

A classic work by Pretko and Radzihovsky [1] showed that the theory of elasticity can be dualised to a higher-rank gauge theory with the elastic defects (disclinations and dislocations) acting as charges. Motivated by it, we show that when the crystal lattice is composed of electrically charged particles, like in the case of a Wigner crystal, the resulting dual theory contains an additional gauge field sourced by vacancies and interstitials [2]. Unexpectedly, we find that upon a condensation of vacancies or interstitials the corresponding gauge field does not become massive – on the contrary, the number of massless modes in the system increases. We dub this mechanism the anti-Higgs mechanism.

Higher-rank gauge theories are closely linked with the physics of fractons, i.e., excitations that cannot move freely through the system without being assisted by other excitations. Thus, I will also give a general introduction to the physics of fractons and show how it can be applied to study the motion of elastic defects.

[1] “Fracton-elasticity duality”, M. Pretko and L. Radzihovsky, Phys. Rev. Lett. 120 (2018)

[2] “Quadrupole gauge theory: anti-Higgs mechanism and elastic dual”, A. Głódkowski, P. Matus, F. Peña-Benítez, L. Tsaloukidis, arXiv:2411.19350