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
2
answers
69
views
Can Bose-Einstein condensates and Fermionic condensates survive for long periods of time in space?
Imagine we have a cold region of the universe, almost devoid of matter and radiation. Or perhaps in a future universe where the CMB has "cooled" down to sufficiently low "temperatures&...
0
votes
0
answers
39
views
Chemical Potential of a Fermionic System
If the chemical potential of a fermionic system is $0$ at temperature $T=0$, will it be zero at any arbitrary finite temperature?
3
votes
1
answer
88
views
How to find plasmon from Landau-Silin equation?
In David Pine's Theory Of Quantum Liquids: Normal Fermi Liquids, it's said that we can find charged Fermi liquid has plasmon modes easily from Eq. (3.40), replicated as follows:
$$
(\boldsymbol{q} \...
0
votes
1
answer
150
views
Quasi-particle distribution in Fermi liquid theory
In Fermi liquid theory, the quasi-particle is well-defined only near the Fermi surface. However, in calculating specific heat and compressibility, we also assume that the quasi-particle obeys the ...
0
votes
0
answers
57
views
Is (Landau's) Fermi liquid theroy a classical theory?
As a person majoring in condensed matter physics, I frequently encounter Landau Fermi-liquid theory. Almost every literature says that the concept of the adiabatic continuity (to the non-interacting ...
0
votes
1
answer
74
views
Pauli Exclusion Principle in Landau Fermi's liquid theory
I do not understand how Pauli exclusion principle helps us to understand the excitations in Landau Fermi's liquid theory. In Landau Fermi liquid theory, Pauli exclusion principle and adiabatic ...
8
votes
1
answer
159
views
Can Fermi liquid be obtained by a canonical transformation?
The basic assumption of the Ferm-liquid theory is the one-to-one correspondence between the states of an interacting Fermi gas to those of a gas of non-interacting quasiparticles. The question is ...
1
vote
1
answer
108
views
Is is possible to extract an effective Hamiltonian from a Boltzmann equation (or any other kinetic theories)?
I got kind of confused when reading Xiaogang Wen's famous textbook Quantum Field Theory of Many-body Systems. In Section 5.3.3 the book claims that
From a kinetic theory of Fermi liquid (a Boltzmann ...
0
votes
1
answer
25
views
Gas to liquid phase transitions for electronic matter
Regular atomic matter almost always experiences liquid-gas transition at some temperature (at sufficiently low pressure). Does anyone know if electrons in metals/semiconductors experience a similar ...
3
votes
0
answers
558
views
Hertz-Millis theory and quantum criticality
Hartz-Millis(HM) theory is a model which exhibits quantum phase transition. The HM action following Altland & Simons is given by
$$
S = \frac{1}{\beta}\sum_{\omega_{n}}\int \frac{d^d q}{(2\pi)^d}\...
10
votes
1
answer
898
views
Finite quasiparticle lifetimes in Fermi Liquid Theory
I am trying to clarify a conceptual issue about phenomenological Fermi liquid theory. My confusion can be explained using the following two sentences from Dupuis's many body theory notes, but the same ...
0
votes
1
answer
202
views
Excitations in Luttinger liquids
It's not clear to me what are the elementary excitations of Luttinger liquids. Quoting from Giamarchi's book Quantum Physics in One Dimension:
In one dimension, [...], an electron that tries to ...
2
votes
1
answer
311
views
Bosonization and peculiarities of 1-D systems of interacting fermions
I'm studying bosonization and from what I've understood the main reasons why it's useful are that:
For models such as the Hubbard model the Bethe Ansatz, though it allows to evaluate eigenvalues and ...
2
votes
0
answers
278
views
Pomeranchuk Effect
Pomeranchuk effect poses a paradox of order by disorder phase-transition. The liquid Helium-3 is in a liquid form close to absolute temperature. For high enough pressure, as you increase the ...
2
votes
1
answer
96
views
Mermin's derivation on the existence of zero sound
I have a question concerning Mermin's 1967 paper "Existence of Zero Sound in a Fermi Liquid". The condition on zero sound is given by the equation
$$\lambda_n>\eta^{-1}\int \frac{d\hat{n}}...
1
vote
1
answer
62
views
(Coleman many-body Chapter 8) Validity of near-Fermi-surface approximation
In the Chapter 8 of Coleman's many-body physics book, he argues as follows. In the impurity problem, the approximate self-energy can be written as (8.89). I have no problem until this part. However, I ...
3
votes
1
answer
116
views
Calculating the inelastic quasiparticle lifetime of a screened quantum fluid
I've been studying "Lifetime of a quasiparticle in an electron liquid", by Qian and Vignale. Much of it makes sense, but there is a detail in the calculation of the exchange term that doesn't make ...
2
votes
1
answer
168
views
Energy of Fermi Gas $T>0$
I'm trying to plot $ \frac{E(T)}{N\epsilon_F} $ vs $\frac{T}{T_F}$
I know that the total energy comes from $$ E(T) = \int_{0}^{\inf} \frac{3}{2}\frac{N}{\epsilon_F}(\frac{\epsilon}{\epsilon_F})^{1/2} ...
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 (...
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
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 ...
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 ...
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 ...
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 ...
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
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 $...
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{...
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 ...
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 ...
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 ...