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One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters.

It seems to me that some physicists in the fields often mix the usages of these twos: Strong Coupling, Strong Correlated.

However, in my viewpoint, they are NOT the exactly same, I regard that

$\bullet$ Strong Coupling: implies the large coupling of interactions comparing to the free part of theory. Say, suppose there is a Lagrangian description, then the action $S$ $$ S=S_{free} +g S_{interact} $$ the Strong Coupling means $g >>1$. So this can be the confined phases of QCD, where coupling $g$ of quarks and gluons runs large.

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$\bullet$ Strong Correlated: in my view, usually implies the fractionalization of the elementary particles into fractional quantum numbers. For example, this happens at 1+1D Luttinger liquids, where spin and charge can separated their degree of freedom from the elementary constituents(electrons), but the system needs NOT to be Strong Coupling. i.e. this example is Strong Correlated but NOT Strong Coupling. This is about the fields of Strong Correlated Electron on arXiv.

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My question, so what are other examples of systems that are:

1. YES Strong Coupling and YES Strong Correlated

2. YES Strong Coupling but NOT Strong Correlated

3. NOT Strong Coupling but YES Strong Correlated

See also this relevant post.

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    $\begingroup$ You're right they are not the same. The definition of strong coupling is pretty obvious, but that of strong correlation is much less so. For some people, it means "large correlation length", with the extreme example of critical points (classical or quantum). For other, it just means "a naive/mean-field expansion (weak or strong coupling)" does not work (examples for this: BCS, Bose Mott phases are not strongly correlated). For some (like you?), it means that quasi-particles do not exist. So it might mostly be a matter of definition... $\endgroup$ – Adam Jun 7 '14 at 4:12
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    $\begingroup$ A blog post about this question: condensedconcepts.blogspot.com/2014/02/… $\endgroup$ – Adam Jun 7 '14 at 4:16
  • $\begingroup$ And what about the difference between coupling and interaction? it follows from your post that there's one but you don't comment about it, could you clarify it, please? Also, what it means the $S_{free}$? it includes the kinetic part? $\endgroup$ – cla Jan 5 '17 at 16:01

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