What is a fracton? Recent, in articles on QFT and condensed matter new objects appear -- fractons.
As I understand now, fracton is a particle with restricted motion: for example, such excitations can move only along line.


*If such excitations have restricted motion, how they deal with uncertainty principle?


*Could somebody present simple model, where such excitations appear?


*Also, it is very interesting to understand, which role such excitations play in condensed matter systems?
 A: These[1][2] review papers contain good introductions to fractons.

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*Generally, there is no uncertainty principle for such systems. This is because these fractons are usually emergent particles. For example, we can think of a domain wall excitation in a 1D Ising model as a particle, but this does not have any uncertainty principle associated to it.


*The prototype model for fractons is the X-cube model (gapped). Another class of models can be constructed using tensor gauge theories (gapless). Both of these are discussed in those papers and references therein.


*These systems have many interesting properties. The constrained motion of these excitations make thermalization slow and the dynamics glassy (here), can be used as a system to store quantum information due to its robust sub-extensive ground state degeneracy, and also has interesting connections to toy models of gravity (here). It is also interesting because it is really a new phase of matter we haven't seen before, and has expanded the problem of classification of phases of matter. I am not aware of any experimental realizations of fractons as of now.
