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

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7
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2answers
269 views

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 ...
2
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1answer
64 views

Feshbach resonance in simple terms

I was reading up Feshbach resonances in cold atoms and I was unable to grasp the concept. I will tell you what I have understood. We consider two body scattering processes elastic as well as ...
2
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1answer
69 views

Topological invariant for interacting systems using single particle green functions?

Why Single particle green's function is (preferred) used to find topological for interacting systems? $N_1 =\frac{\epsilon_{ijk}}{24 \Pi ^2} \int dw d^3k G \partial_i ...
1
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1answer
58 views

Electron-Hole Spin Exchange Interaction

I am stuck with this seemingly "simple" Hamiltonian. I am dealing with an exchange term of a Hamiltonian for two different spin species: $$H_\text{exchange} = - \lambda J \cdot S = ...
1
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1answer
70 views

Statistical mechanics vs. many-body theory

Where is the basic difference of statistical mechanics with many-body physics? What are the systems which cannot be studied in statistical mechanics but in many body theory? After all we know ...
0
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1answer
64 views

At what densities the many-body approaches are valid?

Suppose we have a n-particle interacting system with a potential $V=a/(r1-r2)$, it is a pseudo-coulomb potential: you can choose it fermion or boson. Then, at what densities the many-body approaches ...
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1answer
125 views

Can interacting Hamiltonians always be written in second quantized form?

Is it always possible to write interacting Hamiltonian in a second quantized matrix form like we do it for non-interacting form $$H=\sum _{\alpha\beta}C_\alpha^\dagger h_{\alpha\beta} C_\beta$$ ...
8
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0answers
460 views

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 ...
7
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0answers
749 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 ...
4
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0answers
135 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
178 views

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

The single inpurity Anderson Hamiltonian is ...
2
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0answers
66 views

Isotope effect in BCS Theory

The BCS theory for supercondictivity says that the effect of variation of lattice ion mass (M) and its effect on transition temperature is given as $T_{c} \space\alpha\space M^{-\beta}$ . The ...
2
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0answers
74 views

Fermion 1D Hubbard Model ground state in the U = 0 limit

I am trying to determine the ground state of the 1D fermionic Hubbard model at half-filling of $2L$ sites with $L$ electrons with spin-$\uparrow$ and $L$ electrons with spin-$\downarrow$ in the $U=0$ ...
2
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0answers
143 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 ...
2
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0answers
61 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 ...
2
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0answers
103 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
47 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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0answers
41 views

Representation of U(1) on fock space

I am currently reading up on the use of group theory in physics using Peter Woit's book draft (available on his homepage). I do understand the mathematical concepts but have a bit of a problem making ...
1
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0answers
24 views

Creation and annihilation form of hamiltonian to derive a relation between the ac current applied to the crystal and the oscillations of the crystal

in the book "many-particle physics" by G.Mahan in piezoelectric subsection, it uses the second quantization formalism to derive the relation for hamiltonian of the electron-phonon interaction. so ...
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0answers
32 views

Intuition behind modeling quantum impurities as two-level systems

I've been trying to get a basic understanding of quantum impurity problems, starting with the Anderson model. The Wikipedia article (along with some review articles) seems to explain the simplest ...
1
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0answers
88 views

Anderson-Higgs mechanism for the (non-relativistic) $U(1)$ gauge theory under the unitarity gauge

On Page 138, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons by Xiaogang Wen, when he demonstrates the Anderson-Higgs mechanism for the $U(1)$ ...
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0answers
29 views

Lindhard function for surface plasmon

Is there anybody that knows how to calculate the Lindhard function for the surface plasmon (between the surface of two metals of different dielectrics)? What I'm looking for is to find this function ...
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0answers
32 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
162 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
88 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
267 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
118 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!
0
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0answers
20 views

What is the $D_{x^2-y^2}$ symmetry/channel/instabilitied referred to with regards to super-conductivity?

I have been reading various articles on Renormalization group where they compute the flow of some parameter which becomes increasingly attractive and then say that parameter is responsible for Cooper ...
0
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0answers
15 views

Can we use Variational Monte Carlo for degenerate cases?

Consider Simple Example of Bose-Hubbard model $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1) . \tag{1}$$ We can solve this Hamiltonian by Variational ...
0
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0answers
41 views

Wigner-Dyson vs Poisson level statistics in MBL effective Hamiltonian

Many-body localization (MBL) has been a hot topic recently. It was proposed that the MBL system can be describe by the following fixed-point Hamiltonian ...
0
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0answers
37 views

Grand potential $\leftrightarrow$ ground state energy of interacting electrons in a solid

I want to calculate the ground state energy $E_0$ of interacting electrons in a solid at $T=0$ via pertubation theory and Feynman diagrams, i.e. I want to understand the connection between the ...
0
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0answers
25 views

Unitarity of Symmetrisation operators

How can i proove that the symmetrisation operators $S_{\pm}$ are unitary? Defining $S_{\pm}$ on the $N$ Particle Fock Space by it's effect on $|\Psi \rangle=| \Psi_1 \rangle \otimes... \otimes| ...
0
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0answers
80 views

On the Bogoliubov transformation in the BCS

I have a question regarding the diagonalization of the BCS-Hamiltonian using the Bogoliubov-DeGennes-transformation. I hope someone can help me, so I start with the following Hamiltonian, it is ...
0
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0answers
34 views

Why doesn't a quantum pairwise Hamiltonian couple states in which more than one interaction occurs?

This question is about the standard quantum mechanical pairwise interaction Hamiltonian. I'll phrase it in terms of an example using Rydberg atoms, but you could just as well imagine spins (for ...
0
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0answers
10 views

Correct basis for a bosonic bipartite system

Suppose I have two interacting bosonic systems in a double-well potential. They interact, if you want, via a Bose-Hubbard hamiltonian $H_1$ and $H_2$ (where 1 and 2 labels the corresponding ...
0
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0answers
73 views

Simplest fermionic normalized quantum many-particle wavefunction in position representation

What is the simplest fermionic normalized quantum many-particle wavefunction, expressed in the first-quantized position representation, that you can think of? The normal single-particle examples don't ...
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0answers
42 views

electron-electron interactions in 1-D electron gas

The electron-electron interaction contribution to the hamiltonian in $k$-space representation is given by ...
0
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0answers
25 views

What does a completely negative Greens function in frequency mean?

What can a Greens function of frequency mean when it is always negative? The Greens function is for the photons as the following: (It's derived by Matsubara method to enter the thermal effects and the ...
0
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0answers
34 views

Effective mass of almost ideal fermi gas

I am trying to reproduce this famous result of effective mass of almost ideal fermi gas(Galitskii 1958 The energy spectrum of a non-ideal Fermi gas). There are two kinds of ways to find effective ...
0
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0answers
29 views

Two state Hubbard modell

I am given the two state Hamiltonian $$ H = U \sum_{j \in \{L,R\}} n_{j \uparrow}n_{j \downarrow} - t \sum_{\sigma \in \{\uparrow,\downarrow\}}(a_{L \sigma}^{\dagger}a_{R \sigma} +a_{R ...
0
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0answers
47 views

How can I determine the convergence of self energy in Green's function

I want to solve for the Green's function (in the context of many body theory) but I have a question. After the determination of the retarded Green's function and the lesser Green's function we ...
0
votes
0answers
18 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 ...
0
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0answers
54 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 ...
0
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0answers
55 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 ...
0
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0answers
41 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 ...
0
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0answers
54 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 ...
0
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0answers
323 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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0answers
84 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.
0
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0answers
120 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 ...