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I have the impression that some literature say that Galilean invariance is broken by a uniform lattice. That is, although a uniform lattice like a tight binding model is translationally invariant, it is not Galilean invariant.

Could anyone expound this point?

As far as I can see, a discrete translation symmetry is quite similar to a continuum translation symmetry.

ps. Here we have a paper suggesting that a lattice system is not Galilean invariant.

enter image description here

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    $\begingroup$ Which literature? Which page? $\endgroup$
    – Qmechanic ♦
    Commented Jun 11 at 14:02
  • $\begingroup$ By "Galilean invariance" do you mean continuous translational invariance and by "translational invariance" do you mean discrete translational invariance? Please define these two terms. $\endgroup$
    – QPhysl
    Commented Jun 11 at 14:18

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A lattice isn't translationally invariant because if you translate by a vector that does not point from the origin to a lattice site then you do not end up with the same lattice. Therefore, it is not Galilean invariant.

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