Abstract
We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh techniques, we derive the full dissipative dynamics of the system and we recover the experimentally observed diffusion-to-propagation crossover of the phason mode. From a symmetry point of view, the diffusive nature of the phason at long wavelengths is due to the fact that the internal translations, or phason shifts, are symmetries of the system with no associated Noether currents. The latter feature is compatible with the EFT description only because of the presence of dissipation (finite temperature) and the lack of periodic order. Finally, we comment on the similarities with certain homogeneous holographic models and we formally derive the universal relation between the pinning frequency of the phonons and the damping and diffusion constant of the phason.
Highlights
Similar such symmetries exist in the standard effective field theory (EFT) for ideal fluids and zero-temperature solids [12]; our holographic models do not implement the same number of symmetries in the dual field theory side exactly because the internal shift symmetry is not gauged in the bulk [102]
In this work we have built a finite temperature effective field theory for quasicrystals starting from an action principle and exploiting solely the symmetries of the system
The diffusive dynamics is a direct consequence of the fact that phason shifts are symmetries of the system with no associated Noether current nor conserved charge
Summary
Quasicrystals, or quasiperiodic structures, are materials with perfect long-range order but lacking periodicity [44,45,46,47]. In the case of an icosahedral phase, we need for example 6 of them This point is fundamental in the description of quasicrystals and it suggests immediately that aperiodic structures can always be seen as periodic structures in an extra-dimensional space. Let us perform a one-dimensional cut on this lattice defined by a single angle α with respect to the Figure 2: The superspace description for quasicrystals in a 2D → 1D example. A continuous shift of the modulation creates an infinite set of indistinguishable configurations which can be visualized by piling them up on an axis perpendicular to the physical directions This perpendicular direction is called phase space and it is exactly analogous to the perpendicular direction in the superspace description for quasicrystals explained above and depicted in Fig.. We refer the more interested readers to [51,52,53,54,55]
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