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

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How can I measure the stability of a many body gravitational system?

Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
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1answer
21 views

Electronic or excitonic band structure?

Usually, in the papers the electronic band structure for monolayers $WS_2$ is something like in the figure below: As you can see the direct bandgap is around ~2.0 eV. When we excite electrons at the ...
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1answer
95 views

Why is Wick contraction a $c$-number?

It is mentioned in Fetter's Quantum Theory of Many-Particle Systems (in contraction part of section 8 Wick's Theorem), that: contractions are c numbers in the occupation-number Hilbert space, not ...
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121 views

Validity of mean-field approximation

In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where $...
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58 views

Spectral density and Green's function

this is a basic question but from what I can see it has not been asked before. I am reading Nolting's "Fundamentals of Many-Body Physics". He speaks about the spectral density in characterising the ...
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35 views

Is electron phonon interaction important away from fermi surface?

In weak coupling superconductor, the effective electron phonon interaction can be written as $$ H_{eff}=\frac{1}{2}\sum_{q,k_1,k_2,\sigma_1,\sigma_2} V_{k_1,q}C^{\dagger}_{k_1+q,\sigma_1} C^{\dagger}...
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1answer
73 views

Is there anything comparable to many-body localization in classical physics?

I've only just started looking into many-body localization, so this question may come off as a little vague. But my understanding is that it relates to how some quantum systems do not thermalize, as ...
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140 views

Are symmetries of a degenerate ground-state manifold always broken?

If a Hamiltonian has a global symmetry and a degenerate ground state, then in the thermodynamic limit, the ground states $| \psi \rangle$ that are eigenstates of the symmetry operator typically become ...
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56 views

reconstruct the wave-function from one body reduced density matrix?

Given a many body wave-function for a Fermion system, we can calculate the one-body reduced density matrix straightforwardly. Now suppose we know the one-body reduced density matrix, is there a way to ...
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23 views

Is a phason a Goldstone mode?

Suppose we have a lattice system whose ground state is an incommensurate charge-density wave. Strictly speaking, this ground state does not have Goldstone modes because the only symmetry that is ...
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1answer
72 views

A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
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1answer
80 views

Why are periodic boundary conditions used for the derivation of phonons? [duplicate]

I am currently reading "Quantum Field Theory for the Gifted Amateur". In chapter 2 Phonons are introduced as solutions (in k-space) of a coupled harmonic oscillator. In real space the oscillator is ...
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1answer
61 views

Hubbard model within mean-field: three different approaches

While reading doi:10.1016/j.carbon.2012.03.009 , the authors mention three types of Hubbard models within mean-field approximation. The first one describes the electron-electron interaction, and to my ...
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14 views

Creation operators that differ by a reciprocal lattice vector

In very general terms, if you have an infinite lattice of atoms you can describe the physics in terms of creation (and annihilation) operators $\hat{a}_{\mathbf{R}}$, that create (and annihilate) an ...
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3answers
56 views

What physical properties can't be predicted based on index of refraction? [closed]

If I tell you the real and imaginary parts of the index of refraction for all frequencies, name a property that can't be predicted based on that information. If you're assuming this is a gas, specify ...
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1answer
66 views

Methods for handling close approaches in $N$-body simulations

In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
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93 views

How to write the second quantization form of spin-orbit coupling(Dzyaloshinskii-Moriya interaction)?

Spin orbit coupling is the single particle term, so the second quantization form can be written like:$\langle \alpha\sigma|s\cdot(\nabla V\times P)|\beta\sigma'\rangle c^{+}_{\alpha\sigma}c_{\beta\...
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18 views

Magnetic susceptibility in the spin triplet channel

In the literature and articles I sometimes see the phrase magnetic/electric susceptibility(or other kinds of correlation functions) in the triplet channel. I don't know what does it exactly mean. ...
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1answer
38 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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39 views

Construction of Wannier function for optical lattice potential

Parameters of the Bose-Hubbard model require the knowledge of the Wannier functions from the lowets band of the optical lattice potential $V(x) = V_{0}\sin^{2}(kx)$ according to equations: $$J = \int ...
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1answer
53 views

Why do we use the anticommutation relation for particle-hole and chiral symmetries?

In physics we say that a quantity is conserved if its operator commutes with Hamiltonian. For example, in condensed matter systems, when the momentum $k$ commutes with the Hamiltonian $H$ as $[H,k]=0$...
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2answers
85 views

Approximate expression for the ground state of hopping Hamiltonian

In second quantization, the Hamiltonian describing the hopping process between two neighboring sites is given ($N$ - number of particles and $M$ - number of sites) by: $$\hat{\mathcal H} = J\sum\...
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1answer
48 views

Adiabatic transition from superfluid to Mott insulator?

I have a question about the dynamical passage from superfluid to Mott insulator state in the Bose-Hubbard model. Is it possible to go from superfluid region to the Mott insulator by changing the ...
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0answers
55 views

Alternative derivation of Gross-Pitaevskii equation

I wanted to derive time-dependent Gross-Pitaevskii equation in an alternative way, but I don't know if something presented below is allowed. Hamiltonian is the following (I do not assume translational ...
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122 views

time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in the second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
3
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1answer
53 views

What is special about many-body localization as opposed to Mott insulator

What is the difference between localization in a many-body localization system and localization in a Mott insulator? Is the difference that many-body localization is driven by disorder while Mott ...
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23 views

Nonequilibrium Green's functions weakly interacting two-component Bose gas

I am planing to describe time evolution of two-component BEC. I was thinking about non-equilibrium Green's functions, but I don't if the method can be applied to the problem describe below. I know ...
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1answer
74 views

Density of states in a system of interacting electrons

When we are introduced to the density of states in typical band-theory problems we neglect interaction between electrons, and thus we define the density of states of a sigle particle as: $D(E)=2\int_{...
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38 views

Perturbation method for Hubbard hamiltonian

I've got a hamiltonian to solve from perturbation methods: $$H=\underbrace{-t\sum_\sigma\sum_{i=1}^N(a^\dagger_{i\sigma}a_{i+1\sigma}+a^\dagger_{i+1\sigma}a_{i\sigma})}_{\hat H_\text{kin}}+\...
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1answer
55 views

second quantization - time dependent basis

In the second quantization time-independent field operator can be expanded in the orthonormal basis: $$\hat{\Psi}(\mathbf{x}) = \sum\limits_{i}\hat{a}_{i}\ \phi_{i}(\mathbf{x})$$ Time evolution of ...
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1answer
51 views

partition function of the U=0 Hubbard model

I'm trying to derive the following partition function for the U=0 Hubbard model: $Z=\prod_\mathbf{k}(1+e^{-\beta(\epsilon_\mathbf{k}-\mu)})$ My try was to use: $Z=\sum_{\sigma,\mathbf{k}} <\...
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15 views

Two-particle correlation function for Slater determinant

In a paper by Peschel, http://arxiv.org/abs/cond-mat/0212631, he writes: Consider first a system of free fermions hopping between lattice sites. The one-particle correlation function is \begin{...
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42 views

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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55 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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66 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
105 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
46 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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45 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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26 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
70 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} - \frac{...
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63 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] n_{T}(\...
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73 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: $$-\frac{\hbar^2}{2m}\partial^2_{x_1}\psi(x_1,x_2)...
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1answer
44 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) [a^\dagger_{p\alpha}a^\...
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27 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} \frac{1}{\tau_k}=\frac{2\pi}{\hbar}\frac{1}{V^2}...
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78 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
116 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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43 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', q}\sum_{\sigma}|V_q|^2f_{k'}(1-f_{k-q})(1-f_{k'+q}...
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48 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
326 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
190 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 ...