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.
70
questions
1
vote
1
answer
62
views
(Coleman many-body Chapter 8) Validity of near-Fermi-surface approximation
In the Chapter 8 of Coleman's many-body physics book, he argues as follows. In the impurity problem, the approximate self-energy can be written as (8.89). I have no problem until this part. However, I ...
- 1,081
3
votes
1
answer
116
views
Calculating the inelastic quasiparticle lifetime of a screened quantum fluid
I've been studying "Lifetime of a quasiparticle in an electron liquid", by Qian and Vignale. Much of it makes sense, but there is a detail in the calculation of the exchange term that doesn't make ...
- 2,665
2
votes
1
answer
168
views
Energy of Fermi Gas $T>0$
I'm trying to plot $ \frac{E(T)}{N\epsilon_F} $ vs $\frac{T}{T_F}$
I know that the total energy comes from $$ E(T) = \int_{0}^{\inf} \frac{3}{2}\frac{N}{\epsilon_F}(\frac{\epsilon}{\epsilon_F})^{1/2} ...
- 27
0
votes
1
answer
103
views
Is two dimension equal to three for bosonization?
I have been reading about bosonization lately and really appreciated Luttinger liquid bosonization in 1 dimension. Also, I got interested in higher dimensional bosonization but I only find Haldane's (...
- 161
2
votes
1
answer
252
views
Negative curvature of zero sound dispersion
In the theory of a Landau-Fermi liquid, one of the major predictions is the dispersion of zero sound. From the linearized kinetic equation, we know that the dimensionless dispersion $s$ is given by
$$ ...
- 2,665
2
votes
1
answer
495
views
Non-Fermi Liquids
In Fermi liquid theory, the assumption made (to my knowledge) about the status of quasi particles from the field theory point of view is that the self energy $\Sigma$ in the interacting theory does ...
- 349
7
votes
1
answer
733
views
Why gapped systems are called incompressible?
I study quantum Hall systems and I haven't studied Fermi liquid theory yet. But I understand the concept of having gap or being gapless. But why do we use the term incompressibility to correspond the ...
- 331
3
votes
1
answer
469
views
Why do we have to introduce quasiparticles in the Fermi liquid theory
Why is it necessary in Fermi liquid theory to introduce quasiparticles? I understand the notion of system where someone can turn on the interactions slowly (i.e., adiabatically), but I do not ...
- 437
2
votes
1
answer
400
views
Is there a physical meaning of the Fermi liquid parameters
In Fermi liquid theory we define two parameters $F_l^s = VN(\epsilon_F)u_l^s$ and $F_l^a = VN(\epsilon_F)u_l^a$ where V is the fermi-volume, $N(\epsilon_F)$ the density of states at the Fermi energy ...
- 437
0
votes
0
answers
103
views
Fermi liquid/gas and Goldstones
Often, we say that the low-energy excitations of a quantum system that spontaneously breaks certain symmetries is described by Goldstone bosons. It is also well-known that Fermi liquids and gases are ...
- 1,083
1
vote
0
answers
154
views
Temperature Dependence of the Kubo Formula
I'm trying to calculate the DC conductivity of a Renormalized Fermi Liquid with Green's function
\begin{equation}
G(i\omega,k)=\frac{Z}{i\omega-Z\tilde{\epsilon}_k-ig\omega^2}
\end{equation}
where $...
- 4,827
1
vote
0
answers
105
views
Marginal interactions for Fermi surfaces
I am struggling to understand Polchinski’s derivation (https://arxiv.org/abs/hep-th/9210046) of the conditions for marginality of the 4-fermi operator.
For a scattering process $(\mathbf{p}_1,\mathbf{...
- 169
2
votes
1
answer
212
views
Momentum distribution Fermi liquid and spectral representation
In a Fermi liquid the momentum distribution shows a jump at the Fermi surface, i.e.
\begin{equation}\langle n_{k_F-\delta k} - n_{k_F+\delta k}\rangle = Z_{k_F}\end{equation}
with $Z_k$ the strength ...
- 341
2
votes
1
answer
1k
views
Are there examples of nondegenerate Fermi gases?
A degenerate Fermi gas is an ensemble of fermions with very low interactions and at temperatures that are low enough (lower than Fermi temperature). Most of the examples in the literature are about ...
- 5,568
12
votes
1
answer
668
views
What "transformations" did Abrikosov use in 1958 to get the famous $11-2\log{2}$ result in fermi-liquid theory?
How does one obtain the final integral expression in the appendix of Abrikosov and Khalatnikov's 1958 paper: $\ \ \ $ "Concerning a model for a non-ideal fermi gas" $\ \ \ $ ???
Below, in Bold, I ...
- 121