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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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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Theoretical construction of the He-3 phase diagram from Landau-Fermi liquid theory

The phase diagram of He-3 is well known at this point, with a clear superfluid phase, gas phase, and "normal" Fermi liquid phase (see below from Wikipedia): However, the majority of the discussion on ...
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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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45 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 (...
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95 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 $$...
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108 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 ...
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122 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 ...
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111 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 ...
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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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104 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 ...
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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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169 views

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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243 views

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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355 views

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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621 views

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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380 views

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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The validity of infinite many Conformal Field Theories on the Fermi surface

The naive $2$-dimensional Fermi sea in $k$-space (with a convex structure and positive Gaussian curvature, some nice properties, etc) in $2+1$-dimensional spacetime may be viewed as an infinite ...
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Conventional Landau orders and non-conventional orders in the pseudogap of cuprate

What kind of conventional Landau orders have been seen in the pseudogap phase of cuprate? Such as Spin-Density Wave, Charge-Density Wave, etc? What are the most influential/representative journal Refs ...
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Why is the density of the Fermi gas in a neutron star not changing the potential depth caused by the strong nuclear interaction?

In some textbooks, the neutron star is explained as a degenerate Fermi gas. To calculate the degenerate pressure of the neutron fermi gas the average Energy of a neutron, U is calculated when the ...
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The “dangerous” fixed points for Renormalization Group

What is the definition of dangerously irrelevant renormalization-group (RG) fixed point? What are some examples of dangerously irrelevant RG fixed points? Do we also have the use of dangerously ...
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Total energy of a simple fermi gas

I am a student and working on a fermi gas problem. I already figured out how to calculate the fermi energy of my idealized (no interactions) fermi sphere gas of radius R, but now I want to find out ...
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Experimental confirmation of the finite jump of the occupation number at the Fermi surface

It is a well-known result in Fermi-liquid theory that the occupation number has a finite jump at the Fermi surface. But, is it confirmed experimentally?
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What is the shape of a band electron in momentum space?

Band electrons occupy adjacent sharply defined momentum states that in xyz space take the form of a spectrum of wave functions. These wave functions span the entire xyz volume of any compact unit of ...
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Spin of quasi-particles in a Fermi Liquid à la Landau

I'm having troubles with understanding the motivation underlying the fact that a quasi-particle in a Fermi liquid à la Landau alway has spin 1/2. In section 1.1 of Landau's Theoretical Physics, volume ...
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What is a marginal fermi liquid in a nutshell?

I would like to know what are the main differences between the normal Fermi liquid theory and a marginal fermi liquid theory. What kind of systems can be described by the marginal liquid theory? What ...