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

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how to construct self-energie diagrams

I am working on self-energie and feynmann diagrams. they are not very easy to get but i think i am starting to understand how it works but of course i am not realy sure.and before going any further i ...
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48 views

Operator notation?

I'm starting out with many-body quantum theory, second quantization etc. by reading the book by Bruus and Flensberg. In the first chapter they write; "A given local one-particle operator $T_j$ ... ...
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50 views

Green's functions and spectral function

I'm struggling to understand something in the book by Fetter & Walecka, p.295, relating to the causal ($G$), advanced ($G^A$) and retarded ($G^R$) Green's functions, and the spectral function ...
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1answer
45 views

many body wavefunction and exchange correlation

Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these: 1) Books say that the correlation energy is the difference ...
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1answer
32 views

What does a bucked honeycomb lattice mean?

I was going through some literature where they have mention about bucked honeycomb lattice, but I was unable to understand about the bucked honeycomb term.
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38 views

What does a body visible to the human eye moving at constant speed look like in QFT?

In regular $QM$ A single particle is going to have a wave function that solves the free schrodinger equation of energy and momentum such that $$dE/dp = v$$. Obviously the sense of nearness of ...
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20 views

Can you do an n-body simulation in terms of energy and momentum?

An N-body simulation typically works directly in terms of the gravitational forces and accelerations. If you can solve the equations exactly, this is fine, but there are many instances where this is ...
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2answers
46 views

Confusion with poles of single particle green's function / propagator

On p22 of "Green's Functions for Solid State Physicists" by Doniach and SondHeimer, there is the following definition: $$G^0(\omega)=\frac{1}{2M\Omega_0}\left( \frac{1}{\omega-\Omega_0+i\eta} - ...
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45 views

Numerical problem with Hartree-Fock equations for dilute Bose gas

I have to solve the following set of equations self-consistently: $$\begin{align} n_c(\mathbf{r}) & = \frac{1}{g}\left[\mu - V_{\rm ext}(\mathbf{r}) - 2 g n_{T}(\mathbf{r}) \right] \\[3mm] ...
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63 views

Two interacting electrons in infinite square potential - is there a solution?

If one were to look at Schroedinger's equation for two interacting electrons in a one dimensional infinite square well, it would something like this: ...
2
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1answer
37 views

Problem using spin-restricted form of the second-quantized nonrelativistic Hamiltonian

I have a problem that confuses me a lot. The two-electron part of the electronic nonrelativistic Hamiltonian can be written \begin{equation} \frac{1}{2}\sum_{pqrs} (pq|rs) ...
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17 views

Quasi-electron lifetime at Dirac (Weyl) point

I would like to know how one should calculate the electron lifetime with chemical potential at the Dirac point from Fermi Golden Rule: \begin{equation} ...
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67 views

Derivation of open boundary conditions for Non-Equilibrium Green's Function (NEGF)

It is widely claimed that the Non-Equilibrium Green's Function (NEGF) equations for the study of quantum transport have been derived from the many-body perturbation theory (MBPT). Yet the bridge ...
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1answer
62 views

Consider a particle of reduced mass $\mu$ orbiting in a central force with $U=kr^n$ where $kn>0$ [closed]

Consider a particle of reduced mass $\mu$ orbiting in a central force with $U=kr^n$ where $kn>0$. (a) Explain what the condition $kn>0$ tells us about the force. Sketch the effective ...
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37 views

Fermi Golden Rule derivation of quasi-electron lifetime

I wonder if there is a detailed derivation of the quasi-electron lifetime: \begin{equation} \frac{1}{\tau_k}=\frac{2\pi}{\hbar}\frac{1}{V^2}\sum_{k', ...
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38 views

Question(s) Regarding the Lindhard Function

As a theoretical chemist, I'm slightly outside of my element on a project my advisor gave me, so I come to your for help and direction. Basically, he wants me to integrate the imaginary part of the ...
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3answers
160 views

Seemingly a paradox on the eigenstate thermalization hypothesis (ETH)

In the research field of Many-body Localization (MBL), people are always talking about the eigenstate thermalization hypothesis (ETH). ETH asserts that for a isolated quantum system, all many-body ...
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1answer
74 views

Relationship between lesser Green's function and greater Green's function in Keldysh formalism

I wonder if there is any general relationship between lesser Green's function $G^<(t,t')$ and $G^>(t,t')$ in the non equilibrium case, which means they not only depend on the relative time but ...
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1answer
40 views

What is the 'area law' in the context of matrix product states?

I am trying to get into the topic of matrix product states by reading this: A practical introduction to tensor networks: Matrix product states and projected entangled pair states. R. Orús. Ann. ...
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1answer
30 views

Neutralizing Background and Fractional Quantum Hall ground state

The idealized many-body Hamiltonian describing FQH is given by $$ H = \sum_i \left\{\frac{[\vec{p}_i -e/c \vec{A}(\vec{r}_i)]^2}{2m}+V(\vec{r}_i)\right\} + \frac{1}{2}\sum_{i\neq j} ...
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2answers
86 views

Novel atomic clocks: can quantum and many-body effects help?

I am trying to learn if there are any proposals concerning the application of quantum and many-body effects to atomic clocks. From what I understand, optical lattices have been used for timekeeping ...
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0answers
49 views

Inuitive analogy for localization?

I'm looking for a plain English analogy for electron/wave localization. And in particular weak localization and Anderson/strong localization. Is it possible to describe these phenomena in simple terms ...
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63 views

Correspondence between variational method and Feynman diagrams

There are two ways to look at the Hartree or Hartree-Fock equations. One method relies on the variational method for a particular type of the probe function and the second one originates from ...
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3answers
246 views

Perturbative series for bosons

I have recently read that ... the perturbation series ... is valid only when the perturbed state is qualitatively similar to (or ‘has the same symmetry as’) the unperturbed state. This means ...
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1answer
90 views

What are skeleton diagrams and what is their use in qft and many-body physics?

How does one construct skeleton diagrams from specific Feynman diagrams (e.g. for the electronic Green function in QED and in many-body gases, for the polarization function, for the vertex function, ...
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59 views

Two axis twist spin squeezing Hamiltonian

According to Kitagawa-Ueda (http://journals.aps.org/pra/abstract/10.1103/PhysRevA.47.5138), two-axis counter-twist (TACT) spin squeezing achieves maximal noise reduction. I simulated the scenario ...
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1answer
53 views

Phase diagram of gauge + matter theories

I am looking for some notes/reviews on confinement and Higgs phases suitable for Fermionic/Bosonic matter coupled to Abelian ($Z_2$ or $U(1)$ etc) gauge fields. The purpose is to understand issues ...
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1answer
282 views

Many Body Physics: Hamiltonian block structure and Symmetries

Consider a many body problem of a small cluster, e.g. the 'Hubbard-Cluster' (albeit the question may be of relevance for other Hamiltonians as well): $$\mathcal{H}=\sum_{<ij>\sigma} t_{ij} ...
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34 views

Holography with wave functionals rather than partition functions

Roughly speaking Gubser-Klebanov-Polyakov Witten's (GKPW) prescription in the context of holography tells us partition function of CFT is "equal" to that of the gravity theory in one higher dimension ...
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73 views

Second order pole in Feynman diagrams

Hi, I am calculating density-density correlation function for a homogeneous electron gas. The Green's function for one of three first order connected diagrams(see attached figure) is, $$ ...
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26 views

Coordinate separation and integrability

Why is a system of coupled harmonic oscillators analytically solvable, regardless of dimensionality or particle number, but if the system is coupled by 1/r potentials it is not? I was used to think ...
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1answer
104 views

Derivation of the low-energy effective Hamiltonian

In the quantum mechanics, the Hamiltonian $H$ satisfies the Schroedinger equation $$ H\psi = E\psi. $$ Suppose that $P$ is a projection operator, and $Q=1-P$. The low-energy effective Hamiltonian is ...
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2answers
185 views

Self-teaching Green's function approach to quantum many-body systems

My question is where can I find a good book, review, online course, or all of them for self-teaching Green's function in quantum many-body problems (if it has problems with solutions for ...
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1answer
43 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 ...
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4answers
259 views

How can I add dark matter to my $N$-body simulation?

I've written a simple non-scientific N-body simulation for fun: http://magwo.github.io/fullofstars/ I expected to create something looking like spinning galaxies (there are two invisible very heavy ...
2
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1answer
84 views

Basis states for many-particle system

I'm reading these notes about second quantization. In section 1.4 the author introduces many-particle wavefunctions. But I can't understand how basis are defined here. I know that if $\{\chi_i | i=1, ...
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24 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 ...
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1answer
80 views

A trace formula of two noncommutative operators

In many cases of quantum many-body problems, the Hamiltonian $H$ can always be divided into two parts, i.e. $H_0$ and $H'$. In this occasion, one can systemically calculate the partition function ...
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2answers
248 views

Gaussian integral on a Riemannian manifold

How do I estimate the Gaussian integral $\int d^nx \sqrt{g(x)}~e^{-x^2} $ on a Riemannian manifold $(M,g=det~g_{\mu\nu})$? I've tried to consider $\sqrt{g(x)}$ as an analytic function and expanded it. ...
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1answer
231 views

How is Green function in many-body theory introduced?

Normally, for a (linear) operator $L$ and a DE $$ Lu(x) = f(x) $$ the Green function is defined as $$ LG(x,s) = \delta(x-s) $$ and it is found that $$ u(x) = \int G(x,s) f(s) ds $$ is the ...
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78 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 ...
2
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1answer
108 views

Differentiating between Tensor Networks

I am trying to study tensor networks and their application to quantum phase transitions. However, I had a question concerning the connection between the projected entangled-pair states (PEPS) and the ...
2
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1answer
88 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 ...
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1answer
74 views

What are “correlations”?

When working with realistic two-body hamiltonians, a direct diagonalization is almost always imposible. Thus one usually takes a procedure which yields an approximate solution. A well known approach ...
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31 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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46 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 ...
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41 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 ...
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2answers
71 views

What is the implication of Schmit decomposition?

According to schmidt decomposition if I have pure state $|\psi\rangle$ in the composite hilbert space $AB$ ( both $A$ and $B$ are hilbert spaces of dimension $n$ ) then it can be writen as ...
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29 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| ...
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1answer
168 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 ...