Wigner crystal and FQH effect are both due to strong electron-electron interaction under magnetic field. As we know, Landau's symmetry-breaking cannot be used to describe FQH state. But can it be used to describe Wigner crystal state and which symmetries are broken in Wigner crystal?
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As the name "crystal" implies, the Wigner crystal is defined by broken translational symmetry and the formation of a crystal lattice. This is mentioned in the first paragraph of the Wikipedia entry.
answered Apr 30, 2013 at 4:43
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1$\begingroup$ But the translations are not ordinary translations but magnetic translations, which form a non abelian group (a Heisenberg group). $\endgroup$– jjcaleCommented May 30, 2013 at 10:42
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$\begingroup$ @jjcale: True! Thanks for pointing that out. I didn't process that he was talking about finite magnetic fields. The Wigner crystal state is also possible at zero magnetic field, in which case it would be the usual translational symmetry broken, and presumably the zero and non-zero magnetic field states can be adiabatically connected. $\endgroup$ Commented May 31, 2013 at 16:30