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
0
votes
0answers
24 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
45 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
73 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
28 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
56 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 ...
2
votes
0answers
123 views

Partial trace of matrix product state

I have come accross a formula that puzzles me a bit in the proof of lemma 23 (page 32) of this paper. The authors start from a (translationally-invariant) matrix product state: $$\lvert\psi\rangle := ...
1
vote
0answers
24 views

Is the Andreev-Bashkin effect a beyond-mean-field effect?

I am reading about the Andreev-Bashkin effect, which concerns the current drag from the interaction between two superfluids. Basically, the interaction between two coupled superfluids leads to the ...
3
votes
1answer
149 views

Why gapped systems are called incompressible?

I study quantum Hall systems and I haven't studied Fermi liquid theory yet. But I understand the concept of having gap or being gapless. But why do we use the term incompressibility to correspond the ...
0
votes
1answer
165 views

Understanding second quantized Hamiltonian

Consider an $N$-particle system, for which the Hamiltonian is written in first quantization as $$ \hat H = \hat H_0 +\hat H_I, $$ where $$ \hat H_0 = \sum\limits_{i=1}^{N}\left[-\frac{\hbar^2}{2M}\...
1
vote
1answer
34 views

Taking the speed of light into account during n-body simulation

Currently, I compute the force between two gravitational interacting particles in a simulation with $n$ bodies according to $$F = G\frac{m_1m_2}{r^2}.$$ Doing this, however, assumes that all bodies ...
3
votes
0answers
418 views

A good book on Many-body physics

So, I have two options on my mind: (a) Many-Body Quantum Theory in Condensed Matter Physics: An Introduction by Bruus, Flensberg (b) Many-Particle Physics by Gerald Mahan I have studied a few ...
1
vote
0answers
86 views

How to implement periodic boundary conditions in a $n$-body simulation

I implemented a vanilla $n$-body simulation for educational purposes. As was to be expected, a point cloud collapses towards the middle of the simulation if the particles have zero initial velocity. ...
0
votes
0answers
41 views

Can we invert Density Functional Theory through sufficiently accurate experiment?

The famous Hohenberg-Kohn theorems say that there is a one-to-one mapping between the many-body Hamiltonian, $\mathcal{H}$, of a solid and its ground-state electron density $\rho(\mathbf{r})$. As far ...
1
vote
1answer
57 views

Hamiltonian capable of quantum computation

Suppose we have a 1D spin chain evolving in time according to some Hamiltonian $H_t(p_0, p_1, p_2 \ldots)$, where $p_i$ are classical parameters ``set by the lab equipment". Divide time into discrete ...
0
votes
0answers
28 views

Deriving the expression for one body density

My textbook (Richard M. Martin - Electronic structure) has the following equation for the one body density of a system of $N$ electrons: $$ \langle \Psi | \Psi \rangle n(r) = \langle \Psi | \hat n(r) |...
2
votes
0answers
62 views

Bose-Einstein condensation of interacting bosons

Consider a bosonic Hamiltonian with two-body interactions $$H=\sum_{ij}T_{ij\,}b_i^\dagger b_j+\frac{1}{2}\sum_{ij}U_{ij\,}b_i^\dagger b_j^\dagger b_j b_i,$$ assuming $U_{ij}=U_{ji}$. Suppose the ...
1
vote
1answer
66 views

Why do we require Boltzmann equation to be applicable for only dilute regime?

Why do we force the assumption for Boltzmann Equation to be dilute? Is there any exact formula that defines this DILUTE? and why it has to be dilute? Does it has anything to do with mean free path? (...
3
votes
1answer
78 views

Is there a general behavior of energy gap under renormalization?

Perform real space renormalization on a discrete lattice model with a finite energy gap. Is it always true that under the flow of coarse-graining, the energy gap will only increase? I think the ...
1
vote
0answers
72 views

How to compute a state exhibiting a given entanglement entropy?

We`ve known how to calculate entanglement entropy from a given ground state: make an entanglement cut (that divide system into subsystems $A$ and $B$), take the partial trace and $$S=-\operatorname{Tr}...
2
votes
1answer
302 views

QM Continuity Equation: many-electron in the magnetic field version?

In 1-particle non-relativistic QM we have the continuity condition as a per definitionem property for the 1-electron probability current density for an electron in the magnetic field in a stationary ...
0
votes
1answer
72 views

Number of states in Z2 gauge theory on a finite square lattice

In Wen's Quantum Field theory of many body systems, on page 254, it discusses Z2 gauge theory, and states that Count the number of states in the Z2 gauge theory on a finite square lattice. We ...
1
vote
0answers
46 views

Calculating a correlator

Consider a system of a quantum dot coupled to a metal (tunneling Hamiltonian approach). Creating and destroying electrons in the dot is done with the operators $c_{d\sigma}$ and $c^{\dagger}_{d\sigma}$...
2
votes
1answer
119 views

Physical Hilbert space of dimension $N$ factorial?

In many-body physics, Hilbert spaces are usually equipped with a tensor structure (ie: $\mathcal{H}=\mathcal{V}^{\otimes N}$). If the dimension of local degrees of freedom is set to be $dim(\mathcal{...
0
votes
2answers
61 views

Why propagator in three time intervals can be connected together in the Green function?

In the page 91 of Many particle physics by Mahan, why $S(+\infty,t) C(t)S(t,t')C'(t')S(t`,-\infty)$ in the numerator can be written as $C(t)C`(t`)S(\infty,-\infty)$? And why in the first place the ...
1
vote
0answers
216 views

Generalization of Wick's Theorem

Wick's theorem allow us to write a time-ordering of creation and annihilation operators as a normal-ordering of contractions of these operators. I am studying a system that consists of two kinds of ...
0
votes
1answer
114 views

Level statistics of many body localization

I was calculating some Hamiltonian's spectrum statistics. Namely, I calculated the Hamiltonian's eigenvalues and sorted them in an ascending order: $E_1,E_2,E_3...E_N$. The quantity I calculated is r, ...
2
votes
1answer
162 views

Why do we have to introduce quasiparticles in the Fermi liquid theory

Why is it necessary in Fermi liquid theory to introduce quasiparticles? I understand the notion of system where someone can turn on the interactions slowly (i.e., adiabatically), but I do not ...
0
votes
0answers
122 views

Thermal average of fermionic operators in QFT

Consider the following expression of a thermal average involving fermionic operators \begin{equation} \sum_{\nu, \nu', \sigma, \sigma'}\langle c_{\nu,\sigma}^{\dagger}(t)c_{\nu',\sigma'}\rangle, \end{...
2
votes
1answer
140 views

Is there a physical meaning of the Fermi liquid parameters

In Fermi liquid theory we define two parameters $F_l^s = VN(\epsilon_F)u_l^s$ and $F_l^a = VN(\epsilon_F)u_l^a$ where V is the fermi-volume, $N(\epsilon_F)$ the density of states at the Fermi energy ...
0
votes
0answers
40 views

2-particle hamiltonians numerical solution?

Suppose I have a hamiltonian of the form $$H=\sum_{i,j}c_{ij}a^{\dagger}_ia_j+\sum_{i,j,k,l}v_{ijkl}a^{\dagger}_i a_j a^{\dagger}_k a_l$$ where $a^\dagger_i$ is the creation operator on site i. If $...
1
vote
2answers
159 views

$n$-body problem = many-body problem? [closed]

Are the terms "$n$-body problem" and "many-body problem" synonymous? Or does one refer to a numerical problem an the other to an analytical problem?
1
vote
2answers
97 views

How to derive the macroscopic dielectric function?

I'm following Matteo Gatti's slides to repeat the derivation of macroscopic dielectric function $\epsilon_M$: $$\epsilon_M=\dfrac{1}{\epsilon^{-1}_{\vec{G}=0,\vec{G}'=0}(\vec{q},\omega)}.$$ On page ...
4
votes
0answers
80 views

Lagrangian for system of particles with statistical distribution $f(x_1, …, x_N)$

For system of $N$ particles it is known that it is a good model to take Lagrangian to be (ignoring electromagnetism) $$L = \sum \limits_{i=1}^N \frac{1}{2}(m_i \mathbf{v}_i^2) -U(\mathbf{x}_1, ..., \...
0
votes
1answer
53 views

Has many-body tunneling at the level of nuclei been studied?

In a recent paper, the authors stress the difference between single-body tunneling and many-body tunneling (at the atomic level): "In contrast to the well-studied incoherent single-particle tunnelling,...
2
votes
1answer
119 views

Modifying the Hamiltonian when there is a presence of the Coulomb interaction

Referring to the Hamiltonian of a system of free electrons, $$ H_0= \sum_{\sigma} \int d^3rd^3r' \psi_{\sigma}^{\dagger}(\mathbf{r})\left(- \frac{\hbar^2}{2m}\nabla^2\right)\delta(\mathbf{r}-\mathbf{...
0
votes
1answer
289 views

The overlap of two Slater determinant states

Suppose I have two fermionic number states in different bases, with the same particle number $N$ - call them $|\Psi\rangle$ and $|\Phi\rangle$. In the position basis, I can write the many-body ...
0
votes
1answer
124 views

Contribution of a second-order Feynman diagram for the one-particle Green function

I am studyng how to construct Feynman diagams for the perturbative expansion of the one-particle Green function (or propagator) using the book "A Guide to Feynman Diagrams in the Many-Body Problem". ...
1
vote
0answers
52 views

Why are degenerate ground states interesting?

Studying the Su-Schrieffer-Heeger chain I have learned that the model has two different phases, one which is called topological and the other one trivial. In the notes it says that these phases are ...
3
votes
0answers
86 views

An equivalent computation of a Feynman diagram

A typical second-order diagram for the self-energy gives integrals such as: $$\int \int d \omega^\prime \omega^{\prime \prime} g(\omega-\omega^{\prime})g(\omega^{\prime \prime})g(\omega^{\prime}+\...
2
votes
0answers
102 views

How does the quantum partition function of a many body system relate to that of a single body system

$\DeclareMathOperator{\tr}{tr}$ So from what I understand, if we have a quantum system, described by the Hilbert space $\mathscr{H}$, in thermal equilibrium with a large environment, then the ...
3
votes
2answers
1k views

Bogoliubov transformation for bosons (matrix calculation)

I'd like to know if there is a general numerical method of diagonalizing the bosonic quadratic Hamiltonian below $$H=\sum_{i,j=1}^NT_{ij}b_i^\dagger b_j+\frac{1}{2}\sum_{i,j=1}^N\left(U_{ij}b_i^\...
1
vote
0answers
61 views

Validity of Random Phase Approximation in 2D/3D semimetals

In, for instance, this paper and this one the authors look at many-body effects in two- and three-dimensional semimetals, which have a low-energy quasiparticle dispersion relation of the form $\...
1
vote
1answer
36 views

Potential energy of one dimensional harmonic oscillator at Piers Coleman Book

In the book "Piers Coleman - Introduction to Many-Body Physics (2016, Cambridge University Press)" http://download.library1.org/main/1558000/6a62454463a644d8b5cfa7936cf355de/Piers%20Coleman%20-%...
1
vote
0answers
47 views

Hartree-Fock approximation derivation

Some context: I'm having a hard time deriving the results of the Hartree-Fock approximation. Let $H$ have the form $$H = \sum_{i=1}^{n}\left[\frac{p_{i}^{2}}{2 m}+U\left(\vec{r}_{i}\right)\right]+\...
0
votes
1answer
73 views

Fixing the potential for a quantum particle

I have started studying quantum mechanics and have realised that we can solve the Schrodinger equation for a particle's wave function if we know it's potential energy function. But the potential field ...
1
vote
0answers
52 views

When would an open system reach the steady state calculated from master equation?

From the master equation for density matrix, it seems that one can have steady state solution requiring the derivative of density matrix equals to zero, but I want to know whether a real open system ...
0
votes
1answer
34 views

Any method that can show the time evolution of a open many body system?

the master equation seems is a choice but this method seems only give a mean field result which can not show obviously the effect of specific interaction between particles. So, I am wondering is there ...
1
vote
1answer
468 views

How to obtain the quasiparticle equation from Dyson equation?

The problem is formulated as follows: Dyson equation for zero temperature Green's function: \begin{equation} \left[ i\dfrac{\partial}{\partial t_1} - h(\vec{r}_1) \right] G(1,2)-\int d3 \Sigma(1,3)G(...
1
vote
1answer
95 views

How to derive the vertex function from mass operator in Hedin's equations?

I am stuck from the mass operator to vertex function in the derivation of Hedin's equations. The problem could be organized as follows: Mass operator: $$M(1,2)=i\hbar\int d(34)v(1^+,3)\dfrac{G_1(1,4)}...
0
votes
2answers
321 views

Using the Slater determinant to find the associated antisymmetric wavefunction

My lecture notes read: If there is one electron in the ground state, one in the first excited state, and one in the second excited state, why can we not instantly assume then, that: $$\phi_{n_i}(x_j)...

1 2 3
4
5
12