# Why symmetry breaking a paradigm whilst not describing Fermi liquid?

by nonequilibrium
Tags: describing, fermi, liquid, paradigm, symmetry, whilst
 P: 1,355 Hi! So I'm a bit confused: first off, does Fermi liquid theory have "order". I suppose it depends on how you define order. But in case it does, is it described by symmetry breaking? From what I read, I think it does have order which is not described by symmetry breaking. But then I have trouble understanding why Landau symmetry breaking was regarded as a paradigm for so long if another theory by Landau, i.e. Fermi liquids, did not fit it! (yes I know the paradigm is now overthrown too by topological order but that's not relevant here)
 Sci Advisor P: 3,117 In liquids, like in any matter with finite density, e.g. Galilean invariance is broken which leads to the appearance of sound waves as Goldstone bosons of the broken symmetry. If you could be more specific about which order you are talking it would be easier to determine whether it corresponds to some symmetry.
 P: 1,355 Hm, is Fermi liquid not precise enough? http://en.wikipedia.org/wiki/Fermi_liquid_theory
P: 130

## Why symmetry breaking a paradigm whilst not describing Fermi liquid?

 Quote by nonequilibrium Hi! So I'm a bit confused: first off, does Fermi liquid theory have "order". I suppose it depends on how you define order. But in case it does, is it described by symmetry breaking? From what I read, I think it does have order which is not described by symmetry breaking. But then I have trouble understanding why Landau symmetry breaking was regarded as a paradigm for so long if another theory by Landau, i.e. Fermi liquids, did not fit it! (yes I know the paradigm is now overthrown too by topological order but that's not relevant here)
Is your question whether the Fermi liquid is a state with an order different from the Fermi gas, or whether you can have phase transitions in the Fermi liquid? If it is the latter, then yes, you can have instabilities that lead to magnetic ordering or pairing. If it is the first, I think the point is that the models are adiabatically connected, so there is no change of state or order. It's just that in one case you have a metal with very weak electron-electron interactions, and in another the interactions can be quite strong.

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