# Questions tagged [many-body]

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

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### Why do we go beyond two-body interaction?

Actually, my question is why do we study many-body interactions. I have just started working in Fractional quantum Hall systems. There we have Coulomb interactions between electrons, which we know is ...
564 views

### Mean-Field Theory in Second Quantization Formalism

Consider the Ising model in statistical physics $$H=-J\sum_{\left<i,j\right>}s_{i}s_{j}-\mu h\sum_{i}s_{i}$$ In this case mean-field approximation is done by replacing the surrounding spins ...
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### How field operator $\Psi^\dagger(\mathbf r)$ transform under translation?

In many-body quantum theory, many literatures say that the Green's function $G(\mathbf r t, \mathbf r' t')$ can be written as functions of $\mathbf r-\mathbf r'$, and of course $t, t'$ when the system ...
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### How to apply Wick's theorem in Anderson model

I'm trying to solve the non-interacting single impurity Anderson model where we consider free electrons in a conduction band: $$H_{cond} =\sum_k \varepsilon_k c_k^\dagger c_k$$ and an impurity with ...
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### Explaining friction using Hamiltonian mechanics

I have heard the opinion that it is a good assumption that microscopically all forces are actually conservative so in principle all classical mechanics problems could be solved using Lagrangian / ...
64 views

### reaching from $\hat{A}=A_{\alpha\beta}|\alpha\rangle\langle\beta|$ to $\hat{A}=A_{\alpha\beta}a_\alpha^\dagger a_\beta$

In quantum mechanics we learn that an operator in a basis can be represented as $$\hat{A}=\sum\limits_{\alpha,\beta}A_{\alpha\beta}|\alpha\rangle\langle\beta|.$$ But in many-body physics we suddenly ...
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### Renormalization of sine gordon theory

So assume that we have a usual sine gordon theory in the the theory we have a term in the hamiltonian $$\frac{yu}{2\pi\alpha^2}\int dx \cos(\sqrt{8}\phi_\sigma(x))$$ where $\alpha$ is cut off ...
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### Proving the collapse of a many body system (Fetter and Walecka problem 1.2)

I was trying to solve the problem 1.2 from Quantum theory of many-body systems by A. Fetter and J. D. Walecka. I succeeded in the first part, obtaining the suggested formulation for the expectation ...
283 views

### Resource recommendation: Tensor Networks

I want to learn tensor network methods for condensed matter systems. I went through some basic papers (i.e. 1,2) and come to know that there are many things (i.e. different math, tensors, ...
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### Debye screening in $\mathbb{R^d}$

Consider the Poisson-Boltzmann equation $$\nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right)$$ which models the electrostatic potential in a spherically symmetric ideal gas of ...
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### What is the difference between many body theory and quantum field theory methods in condensed matter?

I am starting to studying condensed matter theory and I do not understand if Many-Body Quantum Mechanics and Quantum Field Theory are just synonyms or are two different methods. It seems to me that ...
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### Self-energy that does not obey sum rule

Analytically, I calculated a self-energy $\Sigma(\omega)$, for which I verified that 1) $\text{Im}\big[\Sigma(\omega)\big] \leq 0$ for all $\omega$ and specifically $\text{Im}\big[\Sigma(0)\big] = 0$,...
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### The notion of “Mobility Gaps” in the context of Anderson Localization

In the context of Anderson Localization, I heard statements such as the following: "Due to disorder, there is a broadening of the bands. Although spectral gaps between continuous bands may shrink or ...
186 views

### The Pauli exclusion principle and the Pfaffian

We are talking about spinless fermion many-body wavefunctions. The determinant is a very nice structure for the Pauli exclusion principle, this is because when two single-particle states are the same,...
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### Proving equivalence of first and second quantisation (Pathria's way)

I'm trying to solve problem 11.1 form Pathria R. K. & Beale P. D. - Statistical mechanics book (the hyperlink will get you straight to the page of the problem). The point (b) is to show the ...
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### Many-body quantum tunneling: Is quantum tunneling sensitive to decoherence?

If we have a many-particle System that is strongly correlated, the tunneling probability can significantly increase; see this article here: https://www.sciencedaily.com/releases/2014/06/140612142215....
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### How to evaluate the matrix element of coulomb repulsion term between electrons in an atom suing spherical harmonics multipole expansion?

This is a lecture notes take from the following link on numerical calculation of atomic physics:http://www.phys.ubbcluj.ro/~lnagy/pdf/1curs.pdf I am trying to evaluate the two electron matrix element ...
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### What's the physical meaning of the kinetic Green's function?

I'm struggling to understand the physical meaning of some of the Green's functions relations. Especially the relation known as the Kinetic Green's function. Which by definition is the sum \$ G^{K} = G^{...
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### The common wavefunction and annihilation of 1 photon [closed]

QM says that if we have many particles they have a common wavefunction. Also QM says that when you measure a particle or observe it, you collapse its wavefunction. That must be a logical mistake. Now ...
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### What tools from quantum information can we use to detect the ergodic to many body localization phase trasnsition?

So is there any specific quantity which depends on the density matrix of the excited eigenstates can detect the ergodic to MBL phase transition? Can anything other than half chain entanglement entropy ...
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### Majorana Fermion Coherent States

I was wondering if there are coherent states for Majorana operators, so, states that fulfill the relation \begin{align} \hat{\gamma}_A |a,b\rangle &= a |a,b\rangle \\ \hat{\gamma}_B |a,b\...
259 views

### Procedure for Effective Hamiltonian using Perturbation Theory? (Bilayer Graphene model)

Sorry if this is a dumb question as I'm just starting out, but in this paper https://arxiv.org/pdf/1803.08057.pdf on Twisted Bilayer Graphene, the authors claim to use "standard perturbation theory" ...