Questions tagged [fermi-liquids]
Fermi liquid theory (also known as Landau–Fermi liquid theory) is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956.
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Infrared cutoff in the Kramers-Kronig relation for the marginal Fermi liquid
I am going through Andre-Marie Tremblay's derivation of the real part of the self energy in his lecture notes on the many-body problem. On page
254, if we take the imaginary $\Sigma''(k,\,\omega)\sim \...
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The formula for the average number of fermions $\langle N \rangle$
In the context of Fermi gases (or fluids in general), one would typically in the grand-canonical formalism use the formula
$\langle N \rangle = -\frac{\partial \psi}{\partial \mu}$, where $\psi$ is ...
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Why do we study fermi system at half-filling state?
I am reading Shankar's paper on RG for interacting fermions and in the paper, all study is done on Fermi system at half-filling state. Is there any specific reason why? Also, does it make a different ...
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Second quantisation of interaction potential (Fermions)
If we start with an interaction Hamiltonian for fermions in second quantised form:
$$
H_\text{int} = \frac{1}{2} \int d^3r \int d^3r' V(|r-r'|) \hat{n}(r)\hat{n}(r')
$$
where $\hat{n}(r)=c^\dagger(r)...
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Wilsonian RG approach to Fermi liquid theory
In modern terms, Landau's theory of Fermi liquids is understood as the fixed point of a Wilsonian RG as one scales towards the Fermi surface.
Shankar and others use the RG interpretation to explain ...
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Stress-energy Tensor of a Fermi Liquid
On page 24 of Baym and Pethick's Landau Fermi-Liquid Theory book, they mention that the stress tensor is given by
$$ \Pi_{ij}=T_{ij}+\delta_{ij}\left(\sum_{\sigma}\int \frac{d^3 p}{(2\pi \hbar)^3}\...
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How can density functional theory (DFT) be understood in many body perturbation theory (MBPT) language?
Many body interacting fermions problems are formulated in the many body perturbation theory language using Feynman diagrams and imaginary time formalism. To the best of my knowledge the kinetic energy ...
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How is mass renormalization in heavy fermion materials differnt from a normal Fermi Liquid?
In normal fermi liquid theory, I saw that the mass is renormalized as
$$ \frac{m*}{m}=1+\frac{F_0}{3} $$
Recently I saw a couple talks on heavy fermion materials. One described, the fermi liquid ...
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Feedback effect of interactions : No interactions between quasiparticles if no external field?
I am working with Coleman "Introduction to many body physics".
In the chapter 7 (pages 131-132) we deal with Fermi liquid and they talk about the Feedback effect of interactions of the quasi ...
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Quasiparticle density of states : how to give it a meaning as the quasi particle are interacting?
There is something I don't understand about quasiparticles density of states.
I work with the book "Introduction to many body physics" from Coleman.
When he introduces the quasiparticle he does the ...
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Volovik's argument and superconductivity
In Volovik's book he describes the Fermi surface as a vortex in energy+momentum space. Due to a winding number the Fermi surface is topologically protected.
I don't understand how the above ...
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Derivation of response function from dynamic form factor
In the book The theory of quantum liquids by Pines and Nozzieres, I have trouble understanding how one goes from formula 2.58 to formula 2.62 and 2.63 on page 99.
So,one defines the response ...
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Unitary Fermi Gas vs. Fermi Liquid
The unitary limit of a Fermi gas is described here as when the scattering length is comparable or exceeds the interparticle distance. For $ak_F<0$, this is the BCS limit of a weakly interacting ...
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Why quasiparticles do not decay in finite system in random phase approximation?
I have tried to apply the conventional recipe of calculating electron self-energy part $\Sigma$ in the random phase approximation (RPA) to the case of finite system and obtained $\mathrm{Im}\,\Sigma=0$...
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Fermi Liquid Theory Reference
I am trying to study Fermi liquid theory as a primer to understand what so-called non-Fermi liquids are. In particular, I want to understand the predictions of Fermi liquid theory (such as temperature ...