Many body covers questions about systems consisting of a great number of particles and techniques used to tackle them.

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Combining two finite number fock spaces into one

Say I have two separate systems of identical Bosons, one with N Bosons the other with M. System one is described by a state $|\psi_1\rangle$ the other with $|\psi_2 \rangle$ which are expressed in a ...
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2answers
73 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
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1answer
236 views

Why is the Wick contraction in HFB or BCS equal to a single-particle density?

I'm trying to understand how in Hartree-Fock-Bogoliubov (HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem". ...
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1answer
149 views

Confused by Many-Body Formalism: Creation/Annihilation to Field Operators

I'm going through an introduction to many-body theory and I am getting tripped up on the formalism. I understand quantities such as $\hat {N} = ...
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1answer
88 views

Projection Method in Hubbard model

This is a question from Altland and Simons book "Condensed Matter Field Theory". In the second exercise on page 64, the book claims that if we define $\hat P_s, \hat P_d$ to be the operators that ...
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0answers
113 views

Confusion regarding field operators

Second quantisation of the scalar field leads to an algebra of quantum field operators $$ [\phi(x),\phi(y)] = 0, \ \ [\pi(x), \pi(y)] = 0, \ \ [\phi(x),\pi(y)] = i\hbar \delta(x-y). $$ Where the field ...
4
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0answers
484 views

Why do Fermi liquids have T^2 resistivity?

I have often read that metals that are Fermi liquids should have a resistivity that varies with temperature like $\rho(T) = \rho(0) + a T^2 $. I guess the $T^2$ part is the resistance due to ...
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0answers
139 views

What is Resonance Width? Why we use it to distinguish different Regimes of the Anderson Model

The single inpurity Anderson Hamiltonian is ...
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0answers
40 views

Is that possible to derive Landau-Fermi liquid theory from microscopic equation?

The question arised 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 ...
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0answers
96 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
2
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0answers
91 views

Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of ...
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0answers
45 views

Why the peak of spectrum gets vague when the dimension is lower?

In a many-body system, we can know the spectrum function at a particular temperature from Green function. It means density of states. A peak of spectrum represents one mode. My question is that in the ...
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+250

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
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33 views

How to compute matsubara frequency summation over computer?

Matsubara frequency sum usually takes the following form: $S_\eta = \frac{1}{\beta}\sum_{i\omega_n} g(i\omega_n).$ But in my problem, $g(i\omega_n)$ is a lengthy expression, which can not be ...
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0answers
30 views

Estimation of polarization perturbative term

I'm studying a diagrammatic approach to degenerate electron gas. Now I need to prove that the energy contribution, with an arbitrary potential, of polarization at first perturbative order given by the ...
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0answers
104 views

Good introduction to many-body Green's function via path integral formulation?

Can anyone kindly provide any information on valuable references or books on this topic? It appears to be prevalent in 90s papers on High-Tc superconductivity or quantum Hall effect, especially in a ...
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0answers
77 views

about orthogonal catastrophe

I am reading Wen's book, QFT of many-body systems ( @Xiao-Gang Wen ). I am a little confused about the orthogonal catastrophe introduced in Chap.5. Below Eq.(5.1.6), it is stated that ``the influence ...
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0answers
174 views

What is many body localization?

Is there any good definition of many body localization? It is the property of one state or it is the property of a Hamiltonian? Why does disorder play an important role in many body localization? ...
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0answers
188 views

Mean-field approximation of the disordered state of Heisenberg model

Consider a 1D ferromagnetic Heisenberg model with the Hamiltonian $$\mathcal H=-J\sum_i \vec S_i\cdot \vec S_{i+1}.$$ For $|\vec S|=\frac{1}{2}$, we have the usual fermionic representation $\vec ...
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0answers
98 views

What do 'first moment' and 'second moment' of a canonical operator mean?

Can anyone explain to me what the first and second moments of a canonical operator mean, in the context of 1D harmonic chain? Thank you!
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0answers
8 views

States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...
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0answers
39 views

Wave function of N electrons in a superconductor

Assuming that the wave function consisting of $N$ electrons is $\Psi_{N}(\bf{r_1,r_2,\cdots r_N)}$ then in the presence of a magnetic field ($\bf{B}=\nabla \times A$), how do I show that the current ...
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0answers
29 views

Hartree Fock exchange kernel

I would like to understand, how we calculate the exchange kernel of the Hartree Fock equations for a coulomb potential. So in slide 19 here for example you see the result, but I have not the ...
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0answers
20 views

Determining a roton minimum from a dispersion relation

I'm currently struggling with a conceptual question in a homework assignment, I'm wondeing if you could maybe help me to understand it better. Here's the question: In class we used the symmetric ...
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0answers
49 views

How can I describe an equation for multiple objects over time?

Lets say i have $n$ different objects that effects each other only by the classic gravity force. I have their initial locations, masses and velocity's: $$ x_1(0),\cdots,x_n(0) $$ $$ m_1,\cdots,m_n ...
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0answers
137 views

Two-Dimensional Tight-Binding Dispersion Relation

As in my last post, I am doing out a calculation in Giamarchi's Many-Body text: http://dpmc.unige.ch/gr_giamarchi/Solides/Files/many-body.pdf. This time, I am going through the derivation of the ...
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66 views

Wave function interaction

If you have two or more wave functions that represent electrons or other charged particles, how would the force on one be calculated based on the charge of the others.
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92 views

relative phase/sign in $\Psi$ after exchange of composite particles with angular momenta

I'm reading Quantum Liquids by A.J. Leggett and became confused by the following statement in the first chapter. Consider now a pair of such identical atoms. In the absence of appreciable coupling ...