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 there a physical meaning of the Fermi liquid parameters

In the 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 ...
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Connection between Matsubara frequencies and Landau Quasiparticle Interpretation

In a zero-temperature Fermi liquid, I understand that Landau quasiparticles correspond to poles in the interacting retarded Green's function, with the quasiparticle weight given by the residue of said ...
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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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63 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{...
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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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545 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 ...
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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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102 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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195 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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78 views

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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270 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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970 views

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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455 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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238 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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664 views

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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462 views

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 ...
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1answer
61 views

What is invalidated when turning on many body interactions in a crystal?

I have just started to think about strongly interacting particles and Fermi liquid theory, and I have two questions. For non interacting particles moving in an potential field, we know that the ...
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803 views

Self-energy of a Fermi liquid

A weakly correlated many-electron system can be viewed in a first approximation as a Fermi liquid, meaning that it behaves similarly to a non-interacting electron gas with renormalized parameters. In ...
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Properties of materials _not_ dependent on fermi surface?

So I'm studying a second solid state physics course where we've covered calculating things like magnetic susceptibility, specific heat and resistivity by considering excitations of electrons around ...
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263 views

Specific Heat of a Fermi Liquid

Let me give a bit of context before asking the actual questions: In the second edition of Condensed Matter Physics, Michael P. Marder derives the specific heat of Fermi liquids in chapter 17.5.4. He ...
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626 views

Landau's fermi liquid theory: With four parameters I can fit an elephant, and with five I can make him wiggle his trunk!

I have no intention of mocking Landau's theory by the quote of John von Neumann (Attributed to von Neumann by Enrico Fermi). I want to understand why we are saying this theory of Landau is remarkably ...
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Is that possible to derive Landau-Fermi liquid theory from microscopic equation?

This question arises from reading Wen's book "Quantum Field Theory of Many-body Systems (Oxford 2004)" p204 To appreciate the brilliance of Landau-Fermi liquid theory, let us look at the many-...
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Strong interacting v.s. Strong Coupling v.s. Strong Correlated

One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters. It seems to me that some physicists in the fields often mix the ...
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No Lagrangian description v.s. No quasi-particle description

This post is aimed to stimulate some discussions. We are familiar with many physical descriptions and theories of the (many-body quantum) system, with both quasi-particle description and Lagrangian ...