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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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 ...
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If $2p$ is the vorticity or vortex charge in a Fermi sea, what is just $p$?
Sorry in advance to ask such a simple question, but I promise I looked around and could not find a straight answer...
I think it might refer to pressure, or a form of pressure, but I am not sure...
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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 ...
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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 ...
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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 ...
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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 ...
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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
$$
S = \frac{1}{\beta}\sum_{\omega_{n}}\int \frac{d^d q}{(2\pi)^d}\...
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Finite quasiparticle lifetimes in Fermi Liquid Theory
I am trying to clarify a conceptual issue about phenomenological Fermi liquid theory. My confusion can be explained using the following two sentences from Dupuis's many body theory notes, but the same ...
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Excitations in Luttinger liquids
It's not clear to me what are the elementary excitations of Luttinger liquids. Quoting from Giamarchi's book Quantum Physics in One Dimension:
In one dimension, [...], an electron that tries to ...
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Bosonization and peculiarities of 1-D systems of interacting fermions
I'm studying bosonization and from what I've understood the main reasons why it's useful are that:
For models such as the Hubbard model the Bethe Ansatz, though it allows to evaluate eigenvalues and ...
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Pomeranchuk Effect
Pomeranchuk effect poses a paradox of order by disorder phase-transition. The liquid Helium-3 is in a liquid form close to absolute temperature. For high enough pressure, as you increase the ...
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Mermin's derivation on the existence of zero sound
I have a question concerning Mermin's 1967 paper "Existence of Zero Sound in a Fermi Liquid". The condition on zero sound is given by the equation
$$\lambda_n>\eta^{-1}\int \frac{d\hat{n}}...
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(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 ...
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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 ...
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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 $$ E(T) = \int_{0}^{\inf} \frac{3}{2}\frac{N}{\epsilon_F}(\frac{\epsilon}{\epsilon_F})^{1/2} ...
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Is two dimension equal to three for bosonization?
I have been reading about bosonization lately and really appreciated Luttinger liquid bosonization in 1 dimension. Also, I got interested in higher dimensional bosonization but I only find Haldane's (...
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Negative curvature of zero sound dispersion
In the theory of a Landau-Fermi liquid, one of the major predictions is the dispersion of zero sound. From the linearized kinetic equation, we know that the dimensionless dispersion $s$ is given by
$$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $...
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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{...
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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 ...
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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 ...
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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 ...
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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 ...
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Fermi liquid vs Fermi gas, when to use either one to model a metal?
I had been taught to consider electrons as a Fermi gas in order to calculate properties (like the heat capacity for instance) of metals even near $T=0K$.
However I'm now discovering Fermi liquids on ...
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What is the relation between the compressibility defined in electron liquid and that defined in thermodynamics?
In electron liquids, the compressibility $K$ is defined as $\frac{1}{K}=-V\left(\frac{\partial P}{\partial V}\right)_N=n^2\frac{\partial \mu}{\partial n}$, where $P$, $V$, $n$ and $\mu$ are pressure, ...
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What's the exact definition for strong correlation in condensed matter physics?
Can we judge or define the strong correlation (for electron system) in condensed matter physics just by the competition of kinetic energy and interaction energy term in the total Hamiltonian? I mean ...
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Discontinuity of Fermi liquid occupancy
In Fermi liquid theory, the electron spectral function is often represented by $$A(k,\omega) = Z\delta(\omega-\epsilon_k)\ + \text{incoherent background} $$ where $Z$ is the weight in the ...
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Hall effect at finite temperature in conventional metals
There are lots of measurements showing strong temperature ($T$) dependence of Hall coefficient ($R_H$) in correlated materials (eg. cuprate superconductors and other oxide materials) and such plots ...
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Why does the free electron theory of metals work?
Free electron theory of metals works unreasonably well in spite of the fact that we neglect the Coulomb repulsion between the electrons. Is there deeper reason why this should work? Somewhere I heard ...
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Failure of Hertz-Millis-Moriya theory for quantum phenomena
In the quantum critical phenomena of condensed matter, the earlier work by Hertz, Moriya and Millis develope the the Hertz-Millis-Moriya (HMM) theory of quantum phase transition.
Naively, they ...
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Fermi "surface" at finite temperature and its measurement in the lab
As we increase the temperature, we know the sharp Fermi surface at zero temperature becomes smeared out at finite temperature $T>0$. (Just think of the Fermi-Dirac distribution, there will be no ...
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