Questions tagged [many-body]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
44 views

Coherent states and classical limit

Consider the coherent state $$ |\phi \rangle = \exp \left( \zeta \cdot \sum_\alpha \phi_{\alpha} a_{\alpha}^\dagger \right) | 0 \rangle.$$ For the case of bosons ($\zeta = +1$), the $\phi_\alpha$'s ...
0
votes
0answers
10 views

How is the translational invariant thermodynamic limit different from periodic boundary conditions?

In a lot of papers physicists simulate spin systems in the thermodynamic limit (infinite chain) with translational invariance using tensor networks etc, in essence very complex methods. For example ...
1
vote
1answer
28 views

Three-body force in Greiner's electrodynamics

In Greiner's book of classical electrodynamics there is an example formula of a three-body force between two charges. For many-body forces the force between two bodies 1 and 2 depends also on the ...
1
vote
0answers
26 views

Feynman's Diagram contribution in Green's Function

I was reading Many Particle Physics by G. Mahan and they calculated the Green's function for electron-phonon interaction using Feynman's Diagram. It was written that Green's function contribution by ...
3
votes
0answers
72 views

Calculating the inelastic quasiparticle lifetime of a screened quantum fluid

I've been studying "Lifetime of a quasiparticle in an electron liquid", by Qian and Vignale. Much of it makes sense, but there is a detail in the calculation of the exchange term that doesn't make ...
0
votes
1answer
41 views

The over-determinant nature for multibody problem [closed]

For an multibody system with N point particles, in Newtonian frame, to solve for the N positions of each particle as a function of time: There is 1 equation for the center of mass. There are $\frac{N(...
1
vote
0answers
26 views

Edge-mode operator for semi-infinite SSH chain

I am asked to show that the SSH-Hamiltonian for a semi-infinite chain with intralattice e interlattice hopping $u$ and $t$, respectively, given by $\hat{\mathcal{H}}=\sum_{n=1}^{\infty}u\hat{c}_{n,A}^...
1
vote
1answer
27 views

Is number of electron conserved in the eigenstates of Kitaev chain?

The definition of Kitaev chain and the solution is in this article: https://topocondmat.org/w1_topointro/1D.html The Hamiltonian has the form: $H = -\mu\sum_n c^\dagger_n c_n -t\sum_n c^\dagger_{n+...
0
votes
1answer
31 views

Charge conjugation symmetry operation on single-particle Hamiltonian

How can I show that given the second-quantized Hamiltonian of a system of non interacting fermions $\hat{\mathcal{H}}=\sum_{\alpha, \beta}\hat{\Psi}_{\alpha}^{\dagger}H_{\alpha\beta}\hat{\Psi}_{\...
0
votes
0answers
21 views

Energy cost for pair of vortices

How should I derive the expression for the energy associated with the formation of a pair of vortices located at $\vec{r}_{1}$ and $\vec{r}_{2}$ in the classical two-dimensional $XY$-model, given by ...
0
votes
2answers
41 views

Level spacing as system size increases

Why does the eigenenergies of a certain system come closer to each other as the system size increases? Is this general for all systems?
0
votes
1answer
42 views

$XY$-model Green function

Considering the two-dimensional XY-model, how should I compute the Green function $G(\vec{r})=\left\langle\phi(0)\phi(r)\right\rangle$ -the scalar field $\phi$ denotes the orientation of the planar ...
0
votes
1answer
39 views

Fourier transform of fermionic creation/annihilation operator

How should I picture the Fourier transform of a fermionic creation (annihilation) operator acting on a site of a periodic, say one-dimensional, lattice? I mean, in a real-space picture, what are the ...
1
vote
0answers
13 views

degenerate link variable configuration in Z2 lattice gauge theory (Wen's QFT book)

I'm reading through Xiao-Gang Wen's Quantum Field Theory of Many-body Systems, and I just begin reading $Z_2$ lattice gauge theory. In page 255, the author constructed a four-fold denegerate (in the ...
7
votes
2answers
191 views

Kubo Formula for Quantum Hall - Derivation and Errors(?)

When one computes Hall conductivity $\sigma_{xy}$, one can show that the zero temperature Kubo formula gives \begin{align} \sigma_{xy}(\omega) = -\frac{i}{\omega} \sum_{n\neq 0} \left[\frac{\langle 0|...
1
vote
0answers
27 views

Designing a many-body physics course [closed]

Preface: This might be an unusual question for this forum. Owing to the lack of a course on many-body physics offered in my department, I am planning to organize a many-body physics study group. ...
-3
votes
1answer
61 views

Permutation as a product of transposition [closed]

On my textbook, the following permutation for 8 particle systems \begin{equation} \mathrm{P}\boldsymbol{=} \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\\ 1 & 2 & ...
0
votes
0answers
40 views

Adiabatic switching, Gell-Mann and Low theorem and Moller operators

Consider the modified Hamiltonian $$ H_{\eta}(t) = H_0 + e^{-\eta |t|} H_I $$ where $\eta > 0$. Consider the interacting picture and the Moller operators obtained by the interaction picture time ...
-3
votes
1answer
111 views

Order of tensor product in quantum mechanics? Why it doesn't matter?

I am looking for a somewhat "official"/accepted proof or rationale on why the order of tensor product doesn't matter in physics but matters in mathematics. In every book of quantum theory (for ex ...
5
votes
0answers
84 views

Does the Mott insulator exist?

The Mott insulator is a system that due to strong electron-electron interactions is an insulator which be a metal by formal charge counting of electrons in the unit cell. Often, the Mott insulator is ...
1
vote
1answer
23 views

How does a thermal propagator work?

I am looking at a propagator in the Hubbard model (in the strong coupling limit) and my timescale is $\beta$. I see that for longer (imaginary) times $\tau$, the particle can propagate further away. ...
1
vote
0answers
39 views

Physical interpretation of the spectral function in a superconductor

Starting from the standard mean-field Hamiltonian of a superconductor, $$H = \sum_{\mathbf{k},\sigma} \epsilon(k) \; c^\dagger_{\mathbf{k}\sigma} c_{\mathbf{k}\sigma} + \Delta \sum_\mathbf{k} (c^\...
1
vote
1answer
50 views

Factors for topologically similar Feynman Diagrams

I am reading Dr. Mattuck's A Guide to Feynman Diagrams in the Many-body Problem and found a rule I didn't see in my other QFT textbooks. It states as: If we are given a diagram, and form a new ...
1
vote
1answer
37 views

Calculation of second-order diagram

Can't figure out how to calculate Feynman diagrams of orders higher than one. One of the simplest diagram of second order is: Integrating over $q_1$ is not a problem because there is $e^{i\omega\...
2
votes
0answers
16 views

Mechanical wave transmission through 3 strings of different medium qualities

How would the motion of waves behave if there are 3 strings joined to each other (as displayed in the fig.) and a wave was started in the string-3? Which would undergo inversion of strings and for ...
4
votes
0answers
51 views

Paths for Learning Keldysh Field Theory [duplicate]

I am an physics undergrad in my pre-final year. Recently, I tried learning some QFT (from the likes of Peskin and Schroeder’s 1st 4 chapters, David tong etc.) and got interested in it’s working in a ...
0
votes
0answers
39 views

Deuteron nucleus, what is the wavefunction (including isospin)?

What is the exact form of the wavefunction of the deuteron nucleus. Without electrons. Only neutron and proton combined to a total wavefunction. In the ket-notation I have something like this: $| \...
0
votes
1answer
43 views

Real-time Green Function in finite temperature

As in standard many-body textbook (at least in my class), we use real-time green function when temperatures is zero, and we use imaginary-time green function when the temperature is finite. My ...
2
votes
1answer
66 views

Relativistic corrections to first-principles Hamiltonian?

In quantum treatments of solids it is common to start off discussions by writing down the "full" first-principles Hamiltonian for a group of electrons and nuclei as $$H = \sum_i \frac{\hat{p}_i^2}{...
1
vote
1answer
58 views

Evaluating integral for Friedel oscillation using branch cuts

I am finding some difficulties understanding the following problem. I have the following logarithm for which I have to identify branch cuts: $$\lim_{\epsilon\rightarrow0}\ln{\frac{(p+2p_F)^2+\epsilon^...
0
votes
0answers
34 views

Time derivative of the polarisation to obtain an integration of the current density

I'm trying to go through some equations In Mahans Many-Particle Physics 2nd Ed. on pg 30 it explains that an alternative form of the current density operator can be obtain by considering the time ...
0
votes
0answers
24 views

Question regarding the derivation of equation for anomalous density

I was reading this paper and have a question regarding the derivation of equation $3.7$ for $\tilde m$ from equation $3.4c$. In particular, I was having trouble seeing why \begin{align} (h^\text{sp}(\...
1
vote
1answer
110 views

Microscopic theory of superconductivity in the language of the vertex function

In Chapter 7 of Abrikosov, Gorkov, and Dzyaloshinski (AGD), the authors cover a microscopic overview of superconductivity, with an emphasis on the poles of the vertex function $\Gamma$. Despite the ...
1
vote
0answers
76 views

Efficient calculation of potential energy of $n$-body system

Consider $n$ bodies which interact solely through Newtonian gravity/Coulomb force, then the total potential energy of the system can be obtained as: $$U =\pm \sum_{1\leq i<j\leq n}\frac{G\alpha_i\...
1
vote
0answers
32 views

Correlation functions and non-bravais lattices

Consider a many-body system characterized by some Green's function $G(\vec{x},\vec{x}',t)$. In the presence of translation invariance, it's natural to work with the Fourier transform of this: $$G(\...
2
votes
1answer
78 views

Negative curvature of zero sound dispersion

In the theory of a Landau-Fermi liquid, one of the major predictions is the dispersion of zero sound. From the linearized kinetic equation, we know that the dimensionless dispersion $s$ is given by $$...
6
votes
0answers
126 views

How to deal with the poles in imaginary axis when applying Matsubara Sums?

The start point of Matsubara Sums is: $$\frac{1}{\beta}\sum_{\omega_n}F(i\omega_n)=\frac{1}{2\pi}\oint_C dz F(z)n(z)$$ where $n(z)$ is the bosonic/fermionic distribution function with the pole $z=i\...
0
votes
1answer
62 views

Expectation value for Bogoliubov quasiparticle operators

While calculating some expectation values for Bogoliubov quasiparticles in the context of the BCS theory of superconductivity, I stumbled across $\langle\hat{\beta}_{\bf{k}\uparrow}^{\dagger}\hat{\...
0
votes
1answer
57 views

Range of the interactions: long/short-range

I have seen in Long/short-range interaction that in scattering theory $𝑟^{−𝑛}$ is a short range potential for $n>1$ and a long range potential for $n\leq1$. Now, why do we say that van-der-Waals ...
1
vote
1answer
58 views

$Z_2$ symmetry breaking in XXZ model

I have a question about an statement that is said in the paper Entanglement and spontaneous symmetry breaking in quantum spin models (Phys. Rev. A 68, 060301(R), (2013)). It is related to the XXZ ...
9
votes
1answer
172 views

Ground state of Hamiltonian

I want to verify explicitly that for $N$ particles in two dimensions the function $f(x)=g(x)h(x)$ where $$g(x)=\prod_{i\neq j} \vert x_i-x_j \vert^{2\beta/N}$$ and $$h(x)=e^{-\beta \sum_{i=1}^N \...
1
vote
1answer
58 views

How to calculate the second order pertubation in an electron gas?

This problem is from the book Quantum theory of many particles systems by Fetter & Walecka (1971), exercise 1.4. Problem discription: The Hamiltonian could be divided into $$H_0=\sum_\limits{\...
1
vote
1answer
71 views

Energy gap in BCS theory

In the context of the BCS theory of superconductivity, which energy gap is one referring to when using the BCS gap equation $\Delta_{\textbf{k}}=-\sum_{\textbf{k'}}V_{\textbf{k},\textbf{k'}}\text{g}_{...
5
votes
2answers
137 views

What are the difference about the concept of polarization and screening in fundamental electromagnetics and many-body physics?

I found that some concepts, such as polarization and screening, met firstly in fundamental electromagnetics, are used in the context of many-body Green's functions in condensed matter physics. I am ...
0
votes
0answers
22 views

How many-body density $n(\vec{r},t)$ can be viewed as a kind of correlation function?

I am reading Martin's book: interacting electrons. In chapter five about the definition of the correlation function, some points about density as correlation function confused me. The author adopted ...
1
vote
1answer
44 views

How can atomic configurations represent excited states of atoms?

My lecture notes on condensed matter physics talk about pseudopotentials of atoms where the core electrons are replaced by an effective potential. This is in the context of DFT. In the lecture notes, ...
0
votes
2answers
46 views

Lagrange multiplier associated with the requirement of constant particle number

I am following Jones and Gunnarsson (1989). In their paper, readers find the following equation that is often used in many-body quantum physics, in particular density functional theory: $$ \frac{\...
2
votes
1answer
27 views

How physical interaction/processes are connected with the information processing?

It is so hard to simulate few particle systems (to deduce information about the next steps of the particles) but those same particles move without spending any resources or concerns in the right ...
1
vote
0answers
35 views

How to construct quasi-local integrals of motion in many-body localized (MBL) phase?

How does a set of quasi-local operators behave as integrals of motion in the presence of disorder to induce an effective integrability into the system? Which principle should we use to construct local ...
0
votes
0answers
33 views

Easy trick to evaluate normal ordering?

In Martin one can find the exercise 1.(i) on p49: Let $\lambda$ be a real number. Show that $$ e^{-\lambda aa^\dagger}=: e^{-(1-e^\lambda)a^\dagger a} :$$, where the $:\dots:$ mean normal ...

1
2 3 4 5
10