Questions tagged [many-body]
Many body covers questions about systems consisting of a great number of particles and techniques used to tackle them.
665
questions
2
votes
1
answer
33
views
How to use Density Functional Theory to get the correct energy spectrum
I'm having some trouble understanding how DFT can be used to obtain results for electronic structure calculations. We can assume that we're studying an $N$ electron atom with a fixed nucleus and want ...
0
votes
0
answers
22
views
Frequency Integration of Green's Function
If one has a Green's Function that has been projected into the Helcity basis (from spin) of the from
\begin{equation}
G(\mathbf{k},\omega)=\sum_s\frac{1}{\omega-\epsilon_{\mathbf{k},s}+\mu+isgn(\omega)...
- 53
0
votes
1
answer
67
views
Why can we distinguish two electrons in different experiments?
Electrons are indistinguishable particles, however, when I set up two independent experiments (at two positions), I can talk about "the electrons in Experiment x". What's going on here?
I ...
- 5,499
2
votes
1
answer
77
views
Fock Space and Coherent state
Can a coherent photon state also belong to the Fock space? If yes, under what conditions? For example I read that
$$\exp\bigg\{-\frac{1}{2}\sum_i|\alpha_i|^2\bigg\}\exp\bigg\{-\sum_i\alpha_ia_i^{\...
- 487
0
votes
0
answers
35
views
Representation of one-body operator in field theory
Section 2.1 Introduction to second quantization, Page No 47 of Condensed Matter Field Theory reads
Representation of operator (one-body) Single-particle or one-body operator $\mathcal{O}_1$ acting in ...
- 10.8k
0
votes
0
answers
20
views
Renormalized Fermi velocity due to Fock term of interacting electron gas
My task is to calculate the renormalized Fermi velocity of an interacting electron gas. That is, I need to evaluate the following diagram in momentum space to obtain the self-energy contribution $\...
- 385
3
votes
0
answers
31
views
Electron density via bosonization/refermionization
I'm currently trying to understand the rigorous construction of bosonization/refermionization via Jan von Delft.
In the constructive approach, we consider a system on a finite $L$ circle and thus in ...
- 1,598
0
votes
0
answers
15
views
How to derive the equations of motion of finite temperature Green function?
I'm having a trouble deriving the equation of motion of a Green function. My understanding of the derivation is the following.
Given a set of fermionic creation annihilation operators
$$\{a_\alpha (\...
- 181
0
votes
0
answers
38
views
How do you get the Jordan-Wigner commutation relations for spin-1/2 fermions?
I am currently trying to figure out how the answer is derived here. I understand that commuation is $[A,B] = AB - BA$. However I am confused how the $\exp(-i\varphi$) acts on the operators $c$ and $c^\...
- 1
1
vote
1
answer
36
views
(Anderson Localization)Time evolution of occupation number of free fermion model
I encounter a difficulty in comouting the time evolution of occupation number. I want to compute the time evolution of occupation number of Aubry-Andre model to show that there exists Anderson ...
- 191
1
vote
1
answer
37
views
Momentum conservation in correlation functions
In Mahan "Many particle physics" the following Hamiltonian is considered in studying electron tunnelling through a junction
\begin{equation}
H_t = \sum_{kp} T_{kp} c^\dagger_k c_p + h.c.
\...
- 113
4
votes
1
answer
132
views
Is the Hilbert-space description of quantum many-body physics misleading and unphysical?
It is well known that any quantum time-evolution of local, time-dependent Hamiltonians can be described using a poly-depth (in number of qubits) quantum circuit (DOI:10.1103/PhysRevLett.106.170501; ...
- 43
1
vote
0
answers
22
views
Correlation functions with different momenta
In Mahan's "Many-particle physics" p.653 the following correlation function is evaluated
\begin{equation}
\Phi(i\omega)=-\sum_{\textbf{k},\textbf{p},\sigma}\sum_{\textbf{k}',\textbf{p}',\...
- 113
1
vote
1
answer
43
views
How can I compute the momentum of a specific quantum particle in a quantum many-body system?
I'm not sure if this question even makes sense in a quantum mechanical context, but I was wondering how does one compute the observed momentum of a specific quantum particle in a quantum many-body ...
1
vote
1
answer
49
views
Overlap between Many-Body States
Let's say we have the two many-body states
$$ |\psi_k\rangle=\left(\prod_{k=1}^n c_k^\dagger\right)|0\rangle ,\qquad |\psi_\lambda\rangle=\left(\prod_{\lambda=1}^n c_\lambda^\dagger\right)|0\rangle \...
- 776
9
votes
1
answer
297
views
Computing functional derivative of exchange-correlation functional
Sakurai and Napolitano's chapter on density functional theory has claims that it is "straightforward" to find $\delta U_{\text{xc}}/\delta n$ for $$U_{\text{xc}}[n]=\int d^3 x n(\mathbf{x})\...
- 135
0
votes
0
answers
43
views
Intuitive Approach to Wick's Theorem
Context
I'm currently reading Many-Particle Physics by Gerald D. Mahan. In section 2.4 it explains Wick's theorem and he gives the example
$$ _0\langle|T \hat{C}_\alpha(t) \hat{C}_\beta^\dagger(t_1) \...
- 776
2
votes
1
answer
66
views
Origins and understanding hamiltonians for free fermions
I am starting to do some work on free-fermionic models, but I am having some problems understanding some things. My professor led me know that the hamiltonian for free fermions without mass in a ...
- 483
0
votes
0
answers
32
views
Difference between the softening parameter in a Plummer model of a star cluster vs. the softening parameter in a softened gravitational potential
I am doing a gravitational N-body simulation of a star cluster. I set up my initial conditions using the Plummer model, which has potential
$$\Phi_P = -\frac{G M}{\sqrt{r^2 + a^2}},\tag{1}$$
where $M$ ...
0
votes
0
answers
28
views
Approximating energy spectra of many-body Hamiltonian
This is related to the previous post here. Although there is no way to diagonalize this Hamiltonian to obtain the exact eigenvalues, is there a way to approximate the eigenvalues of such a Hamiltonian?...
user261609
0
votes
0
answers
36
views
One-body operator in second quantization formalism
I am putting to test the Eq. (B.10) in the appendix of chapter 4 of Grosso solid state physics. This equation introduce the one-body Hamiltonian $G_1=\sum_i{h(r_i)} $ in the many-body representation, ...
- 45
2
votes
0
answers
18
views
Equality of Bose Lattice Hamiltonian and Josephson Array Hamiltonian
I am currently reading the paper Boson localization and the superfluid-insulator transition by Fisher, Weichman, and Fisher. Equation 2.1 defines the Hamiltonian of a Bose Lattice gas as
$$
H = -\sum_{...
user261609
2
votes
1
answer
40
views
Compressing the Hilbert Space in Traditional DMRG
The traditional, non Matrix Product State, formulation of the Density Matrix Re-normalization Group (DMRG) algorithm can be coded in python. Such a code can be found in the following link:
https://...
user261609
0
votes
0
answers
41
views
Argument for flux quantization
I am reading P. Coleman's Introduction to many-body physics. Coleman claims that At large distances, energetics favor a reduction of the circulation to zero
$$\lim_{R\rightarrow \infty}\omega=0$$
...
- 1,703
4
votes
0
answers
50
views
Extension to excited states of Lieb's Theorem for the Hubbard model
Lieb's theorem shows that for the Hubbard model,
$$\hat{H} = -t \sum_{ \langle \mu,\nu \rangle, \sigma} \hat{c}^\dagger_{\mu \sigma}\hat{c}_{\nu \sigma} + U \sum_\mu \hat{n}_{\mu \uparrow}\hat{n}_{\mu ...
- 1,167
1
vote
0
answers
30
views
Plots of Wannier Functions on the Triangular Lattice
I have been looking for quite a long time on the internet for simple plots of Wannier functions (and/or their squares) for a two dimensional potential forming a triangular lattice. A parametrisation ...
- 558
0
votes
0
answers
43
views
Is the tunnelling effect already naturally accounted for in the density functional theory?
Would it be correct to say the tunnelling effect is already naturally accounted for in the density functional theory or the Hartree-Fock formulation of the many-body problem to the Shrodinger equation?...
- 713
0
votes
0
answers
49
views
Why does the density operator in second quantization represent a density?
Usually, in second quantization, the number operator counts the number of particles occupying a given state. For example, for an occupation number state $\psi$, we have that $\hat{n_k}|\psi> = n_k|\...
- 45
1
vote
0
answers
55
views
Fock Diagram Self-Energy with the Hubbard Model
I am dealing with the Hubbard model and I am wanting to compute the self-energy of this Fock diagram, in the case of the Hubbard Model.
I understand the expression from this diagram could be listed as:...
- 53
2
votes
0
answers
44
views
Statistical physics of broken symmetry state?
If we are considering a system, like a paramagnet, above its critical temperature $T_c$ we can statistically describe it using a canonical ensemble:
$$
\langle A \rangle = Tr\left[ \rho A \right]; \...
- 1,515
4
votes
0
answers
152
views
Fourier Transform of Spin operators
Fourier Transform is often used to diagonalize an infinte or periodic lattice Hamiltonian, for example in the tight-binding model
$$
\begin{aligned}H=t\sum_{\langle i,j\rangle}c_{i}^{\dagger}c_{j}\end{...
- 770
2
votes
0
answers
46
views
How do many-body fermionic operators transform under coordinate transformations?
In non-relaivistic many-body physics, sometimes called second quantisation, fermionic fields $\psi(x)$ obey the anti-commuation relations
$$ \{ \psi(x),\psi^\dagger(y) \} = \delta(x-y), \quad \{ \psi(...
- 3,196
1
vote
0
answers
46
views
Linear response theory, but with measurement issue
In the standard linear response theory, the variation of an observable $A$ at time $t$ due to the perturbing Hamiltonian $H'$ is
$$\langle \delta A(t) \rangle = \int_{-\infty}^t dt' \langle [A(t), H'(...
- 691
0
votes
1
answer
37
views
Minimizing Free Energy when considering multiple particles
I am reading an article about Gross-Pitaevskii Equation using a variational method approach. I am confused about a step of the derivation of free energy.
We want to minimize:$$F=E-\mu N$$ and $$E(\psi)...
1
vote
1
answer
82
views
Kubo identity (electrical conductivity) integration
I am deriving Kubo formula using Kubo identity and I am confused that how does the article perform the following steps. On page 8, we have a integration
$$
I\equiv\int_0^\beta d\lambda Tr\bigg\{\rho_0 ...
- 997
0
votes
0
answers
32
views
Approximate analytic ways to obtain self-energy diagrammatically
I am working on a problem that involves calculating a series of Feynman diagrams for the self-energy. In Dyson's equation, assuming a time independent Hamiltonian:
\begin{eqnarray}
G(i\omega_{n})=G_{0}...
- 200
3
votes
1
answer
99
views
How to derive that resistivity is zero from the BCS theory?
The conventional superconductors can be explained using the BCS theory. Usually, the BCS theory is introduced as follows:
We would like to consider the Hamiltonian that describes the system of ...
- 1,515
0
votes
1
answer
80
views
Exact Diagonalization, Jordan-Winger Transformation and the Second Quantization
I am currently study the quantum Ising model with the guide of my supervisor in an undergraduate project. Since my undergraduate courses didn't cover this, I use this paper to as the main material ...
0
votes
0
answers
48
views
Meaning of correlators $\langle A(t)B \rangle$, $\langle [A(t),B] \rangle$, $\langle \{A(t),B\} \rangle$, etc
In quantum mechanics and many-body theory, one often encounters correlators like
$$\langle A(t)B \rangle, \quad \langle [A(t),B] \rangle, \quad \langle \{A(t),B\} \rangle,$$
where $A$ and $B$ are two ...
- 691
0
votes
1
answer
52
views
Pair correlation function for non-interacting spinless bosons
While trying to solve a second quantization exercise regarding a bosonic gas, I've been having trouble trying to understand the $(1-\delta_{\text{pq}})$ term in the decomposition of the following ...
0
votes
0
answers
37
views
Further insight into the pairing tensor for many-body bosonic systems
According to Blaizot and Ripka's "Quantum Theory of Finite Systems", the generalized density matrix is given by
$$R = \begin{pmatrix} \rho & \kappa \\ -\epsilon \kappa^* & 1-\epsilon ...
0
votes
0
answers
42
views
Matsubara sum of thermal Green's function
I need to retrieve a Matsubara sum representation of the thermal Green's function
$$G_{ij}(\tau)=-\frac{1}{Z}\int \mathcal{D}(\overline{\psi},\psi)\psi_i(\tau)\overline{\psi}_j(0)\exp(-\sum_k\int_0^\...
- 45
1
vote
1
answer
99
views
How can a plasma exhibit both quasineutrality and collective motion?
Since, over a Debye Length $\lambda$, very small compared to the characteristic length $L$ of a plasma, a potential due to a source charge is essentially screened, how can plasma particles communicate ...
- 13
4
votes
1
answer
91
views
Is there a well-defined association between abstract linear operators in Fock space and normal ordered polynomials of fermionic operators?
Suppose I have a fermionic Fock space $H$ of dimension $2^n$. If I fix an operator $O$ acting on $H$ that commutes with the number operator $N$, I typically make an assumption internally that such an ...
- 599
1
vote
1
answer
64
views
Is is possible to extract an effective Hamiltonian from a Boltzmann equation (or any other kinetic theories)?
I got kind of confused when reading Xiaogang Wen's famous textbook Quantum Field Theory of Many-body Systems. In Section 5.3.3 the book claims that
From a kinetic theory of Fermi liquid (a Boltzmann ...
- 131
2
votes
1
answer
81
views
Jordan-Wigner Transformations on fermionic system
I've been trying to use Jordan-Wigner Transformations on a given fermionic Hamiltonian. The given Hamiltonian is: $$ \hat{H}= -\sum_{m=1}^{N}(J_z \hat{S}_{m}^{z} \hat{S}_{m+1}^{z} + \frac{J_{\perp}}{2}...
- 23
2
votes
0
answers
55
views
Averaging SYK models and the disappearance of the density matrix
In A strongly correlated metal built from Sachdev-Ye-Kitaev models by Song et al. they wish to calculate the generating function for a system with quenched disorder. In the Keldysh formalism, this ...
- 143
1
vote
0
answers
49
views
Simple explanation of the dynamical mean field theory (DMFT)?
Can someone give me a good reference article or book, that explains the dynamical mean field theory (DMFT) in a simplest possible manner?
I've read quite a lot about the DMFT (and used it), but ...
1
vote
0
answers
99
views
Approximate the two-body density matrix in terms of product of one-body density matrices
Given a set of boson operators $\hat a_\alpha$, i.e. satisfying
$[\hat a_\alpha,\hat a^\dagger_\beta]=\delta_{\alpha,\beta}$, the one-body density matrix
$\rho^{(1)}_{\alpha\beta}$ is defined via the ...
- 785
0
votes
0
answers
101
views
Relation between two-particle Green's function and density matrix elements
In the article https://doi.org/10.1103/PhysRevA.69.054305, the authors used the following relation between the 2-particle density matrix element and 2-particle Green's function to calculate the ...
