Fractons in effective field theories for spontaneously broken translations

Open Access

Fractons in effective field theories for spontaneously broken translations

Riccardo Argurio, Carlos Hoyos, Daniele Musso, and Daniel Naegels

Phys. Rev. D 104, 105001 – Published 1 November 2021

Abstract

We study the concomitant breaking of spatial translations and dilatations in Ginzburg-Landau-like models, where the dynamics responsible for the symmetry breaking is described by an effective Mexican hat potential for spatial gradients. We show that there are fractonic modes with either subdimensional propagation or no propagation altogether, namely, immobility. Such a class of effective field theories encompasses instances of helical superfluids and metafluids, where fractons can be connected to an emergent symmetry under higher-moment charges, leading in turns to the trivialization of some elastic coefficients. The introduction of a finite-charge density alters the mobility properties of fractons and leads to a competition between the chemical potential and the superfluid velocity in determining the gap of the dilaton. The mobility of fractons can also be altered at zero density upon considering additional higher-derivative terms.

Received 17 July 2021
Accepted 1 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.105001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Goldstone bosons Phonons Superfluidity

Spontaneous symmetry breaking

Condensed Matter, Materials & Applied PhysicsParticles & Fields

Authors & Affiliations

Riccardo Argurio^1,*, Carlos Hoyos ^2,†, Daniele Musso ^3,‡, and Daniel Naegels ^1,§

¹Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles, C.P. 231, B-1050 Brussels, Belgium
²Department of Physics and Instituto de Ciencias y Tecnologías Espaciales de Asturias (ICTEA) Universidad de Oviedo, c/ Federico García Lorca 18, E-33007 Oviedo, Spain
³Centro de Supercomputación de Galicia (CESGA), s/n, Avenida de Vigo, 15705 Santiago de Compostela, Spain

^*riccardo.argurio@ulb.be
^†hoyoscarlos@uniovi.es
^‡daniele.musso@usc.es
^§daniel.naegels@ulb.be

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Issue

Vol. 104, Iss. 10 — 15 November 2021

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Images

Figure 1
This figure displays the dispersion relations of the three modes $ω_{1}$ (blue), $ω_{2}$ (red), and $ω_{3}$ (green). They have been obtained by a numerical analysis of the roots of the determinants (3.7) and (4.18). The array of plots is such that each line corresponds respectively to the longitudinal direction ( $q_{y} = 0$ ) and the transverse direction ( $q_{x} = 0$ ). The columns refer to the case of zero and nonzero chemical potential—to make it more visual, the zero chemical plots are the solid curves while the nonzero chemical ones are dashed. All plots are done with $A = 0.125$ , $k = 1.5$ ; the left column is obtained with $μ = 0 = λ$ while the right column is obtained with $μ = 1$ and $λ = 0.5$ . The vacuum expectation value (VEV) $ρ$ is fixed in the $μ \neq 0$ case by the preceding cited parameters but it is not so in the zero chemical-potential case. For practicality, we took the same value for $ρ$ in both cases. Since $k > μ$ , it means that $v > ρ$ . Hence, at low momentum, the green curve is mostly shiftonic while the red curve is mostly dilatonic.
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Figure 2
This figure displays the numerical $ω_{1}$ mode at low momentum, i.e., the $U (1)$ Nambu-Goldstone mode. Both plots represent the same graph and have been obtained with $A = 0.125$ , $k = 1.5$ , $μ = 1$ , and $λ = 0.5$ . On the left, a 3D plot is provided while on the right it is a contour plot.
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Figure 3
This figure displays the numerical $ω_{1}$ mode at low momentum, i.e., the $U (1)$ Nambu-Goldstone mode. Both plots represent the same graph and have been obtained with $A = 2$ , $G = 1$ , $k = 1$ , $ρ = 0.54$ , and $μ = 0 = λ$ . On the left, a 3D plot is provided while on the right it is a contour plot.
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Figure 4
This figure displays the dispersion relations of the three modes (each mode has its own color, as in Fig. 1). The array of plots is such that each lines corresponds respectively to the longitudinal direction ( $q_{y} = 0$ ) and the transverse direction ( $q_{x} = 0$ ). The columns refer to the case of zero and nonzero chemical potential—to make it more visual, the zero chemical plots are the solid curves while the nonzero chemical ones are dashed. All plots are done with $A = 0.125$ , $G = 0.25$ , $k = 1.5$ ; the left column is obtained with $μ = 0 = λ$ while the right column is obtained with $μ = 1$ and $λ = 1$ . The VEV value $ρ$ is fixed in the $μ \neq 0$ case by the preceding cited parameters but it is not so in the zero chemical-potential case. We took the same value for $ρ$ in both cases for practical reasons. We have that $v > ρ$ , hence, at low momentum, the green curve is mostly shiftonic while the red curve is mostly dilatonic. Notice that since $μ < k$ , the identification of the modes for the finite density case matches the one with zero chemical potential.
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Figure 5
This figure displays the numerical $ω_{1}$ mode at low momentum, i.e., the $U (1)$ Nambu-Goldstone mode. Both plots represent the same graph and have been obtained with $A = 2$ , $G = 1$ , $k = 1$ , $μ = 0.5$ , and $λ = 1$ . On the left, a 3D plot is provided while on the right it is a contour plot.
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