Questions tagged [many-body]
Many body covers questions about systems consisting of a great number of particles and techniques used to tackle them.
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Diagonalize two coupling Hamiltonian in second quantization
I want to solve an exercise in Coleman's Introduction to Many Body Physics to understand better exact diagonalization and lattice models:
Find the transformation that diagonalizes the Hamiltonian
...
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1answer
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Equation for $N$-body problem using Jacobi Coordinate
For reference on Jacobi Coordinate used for solving 2-Body problem, I referred Wikipedia Jacobi Coordinate, and on looking at those equation
I can't get the meaning of the symbol q in the equation for ...
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Feynman diagrams: from QFT to condensed matter
I studied Feynman diagrams in quantum field theories and I'm going to study them in the context of condensed matter physics.
In this post Books for Condensed Matter after Ashcroft/Mermin, two books ...
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Are there any gapped systems that aren't invertible?
Assume the following definitions:
A gapped phase of matter is a collection of (quantum-mechanical) systems with a unique ground state and an energy gap to all excitations in the limit of infinite ...
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1answer
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Why is the density of a BEC so low?
I've just begun reading C. Pethick and H. Smith's textbook "Bose-Einstein condensation in dilute gases" (Cam. Uni. Press). In the Introduction, they contrast the density of atoms at the centre of a ...
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1answer
40 views
Behaviour of quantum spins
I am reading the Jordan-Wigner transformation in the book "Introduction to many-body physics" by Piers Coleman. When I read the introduction of this chapter, it is stated that:
Quantum spins are ...
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1answer
85 views
What is the atomic limit?
I am attempting to grasp topological superconductivity for an assignment and in trying to understand what makes a quantum system topological have came across the following paragraph;
"In the case ...
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9 views
Why is the orbital part of the ground state ket of two spin 1/2 particles a direct product?
In Shankar QM on page 406-407 he says that both electrons are in the lowest orbital state $|n=1, l=0,m=0>$ and have opposite spins so the orbital part of the ground-state ket is just the direct ...
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Why are there two magnon propagators in Ferromagnetic system?
I am confused that the authors of ref.[1,2] defined two magnon propagators in the ferromagnetic system with magnon-phonon coupling (which is similar to electron-phonon coupling). They defined ...
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Program for calculating transition amplitudes
I calculated transition amplitudes with MBPT analytically and used Slater-Condon rules. Now I have a very long expression and I would like to solve my matrix elements. Does someone know a program for ...
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1answer
57 views
Why in the BCS ground state the probability amplitudes are taken real?
In some references (see for example Ballentine ch. 18.5) the ground state of the BCS theory is assumed to be
\begin{equation}
|BCS\rangle = \prod_{\bf k} (u_{\bf k}+v_{\bf k}\hat{c}^{\dagger}_{\bf k,\...
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Reference request on Bogoliubov de Gennes (BdG) formalism
I have tried to gain an understanding about the BdG formalism by just following the calculations I found here and there of people bringing their superconducting Hamiltonians into matrix forms but I am ...
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Will more than one composite boson can stay in the same energy state if constituent fermions has moderate entanglement?
Let say we consider two distinguishable fermions(bi-fermions) in compact form. The case when both fermions are existing as free fermions, they will obey Pauli exclusion principle. In other case if ...
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What is the criteria for two fermions to behave as composite boson? [duplicate]
Other than that overall spin for pair of fermions is integral, what are properties needed to make composite boson. In some articles they say fermionshave to be in compact form , so what happens when ...
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$k$-local Hamiltonian with long range entangled ground states?
Is it possible, and if yes, is there a relatively simple example of a Hamiltonian that only has k-local terms but its ground state always has entanglement beyond $k$ sites?
For instance if $H = H_{...
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1answer
84 views
Renormalization of sine gordon theory
So assume that we have a usual sine gordon theory in the the theory we have a term in the hamiltonian
$$\frac{yu}{2\pi\alpha^2}\int dx \cos(\sqrt{8}\phi_\sigma(x))$$
where $\alpha$ is cut off ...
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Proving the collapse of a many body system (Fetter and Walecka problem 1.2)
I was trying to solve the problem 1.2 from Quantum theory of many-body systems by A. Fetter and J. D. Walecka. I succeeded in the first part, obtaining the suggested formulation for the expectation ...
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Resource recommendation: Tensor Networks
I want to learn tensor network methods for condensed matter systems. I went through some basic papers (i.e. 1,2) and come to know that there are many things (i.e. different math, tensors, ...
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Debye screening in $\mathbb{R^d}$
Consider the Poisson-Boltzmann equation
$$
\nabla^2 V(r) = -\frac{1}{\epsilon_0}en\left(1 - e^{e V(r)/k_BT}\right)
$$
which models the electrostatic potential in a spherically symmetric ideal gas of ...
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84 views
What is the difference between many body theory and quantum field theory methods in condensed matter?
I am starting to studying condensed matter theory and I do not understand if Many-Body Quantum Mechanics and Quantum Field Theory are just synonyms or are two different methods.
It seems to me that ...
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51 views
Self-energy that does not obey sum rule
Analytically, I calculated a self-energy $\Sigma(\omega)$, for which I verified that
1) $\text{Im}\big[\Sigma(\omega)\big] \leq 0$ for all $\omega$ and specifically $\text{Im}\big[\Sigma(0)\big] = 0$,...
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1answer
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The notion of “Mobility Gaps” in the context of Anderson Localization
In the context of Anderson Localization, I heard statements such as the following: "Due to disorder, there is a broadening of the bands. Although spectral gaps between continuous bands may shrink or ...
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1answer
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The Pauli exclusion principle and the Pfaffian
We are talking about spinless fermion many-body wavefunctions.
The determinant is a very nice structure for the Pauli exclusion principle, this is because when two single-particle states are the same,...
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1answer
45 views
Proving equivalence of first and second quantisation (Pathria's way)
I'm trying to solve problem 11.1 form Pathria R. K. & Beale P. D. - Statistical mechanics book (the hyperlink will get you straight to the page of the problem). The point (b) is to show the ...
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Many-body quantum tunneling: Is quantum tunneling sensitive to decoherence?
If we have a many-particle System that is strongly correlated, the tunneling probability can significantly increase; see this article here:
https://www.sciencedaily.com/releases/2014/06/140612142215....
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How to evaluate the matrix element of coulomb repulsion term between electrons in an atom suing spherical harmonics multipole expansion?
This is a lecture notes take from the following link on numerical calculation of atomic physics:http://www.phys.ubbcluj.ro/~lnagy/pdf/1curs.pdf
I am trying to evaluate the two electron matrix element ...
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1answer
55 views
What's the physical meaning of the kinetic Green's function?
I'm struggling to understand the physical meaning of some of the Green's functions relations. Especially the relation known as the Kinetic Green's function. Which by definition is the sum $ G^{K} = G^{...
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1answer
58 views
The common wavefunction and annihilation of 1 photon [closed]
QM says that if we have many particles they have a common wavefunction. Also QM says that when you measure a particle or observe it, you collapse its wavefunction. That must be a logical mistake. Now ...
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What tools from quantum information can we use to detect the ergodic to many body localization phase trasnsition?
So is there any specific quantity which depends on the density matrix of the excited eigenstates can detect the ergodic to MBL phase transition? Can anything other than half chain entanglement entropy ...
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About the symmetry of interaction matrix element in superconductivity
In Sigrist, M. & Ueda, K. Phenomenological theory of unconventional superconductivity. Rev. Mod. Phys. 63, 239–311 (1991).
There is equation 2.1 write as below
$$H = \sum\limits_{{\bf{k}},{\bf{s}}...
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Why don't we have a “Cooper pair” of two holes in a superconductor?
The condensate of Cooper pairs is described by a complex scalar field (or the order parameter) which, when quantized can give rise (or is capable of creating) two types of quanta with charges opposite ...
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81 views
Apparent problem in using Wick's theorem to calculate matrix elements of two body operators
In the second quantized notation, a two body operator $\hat{O}$ can be written as
$$\hat{O} = \sum\limits_{x_1,x_2,x_3,x_4} O_{x_1,x_2,x_3,x_4} a^\dagger_{x_1}a^\dagger_{x_2}a_{x_4}a_{x_3} ,$$ where ...
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1answer
38 views
Simulating electrostatics in discrete time steps
I am trying to simulate the motion of several charged particles that are free to move around but have repulsive forces between each other. These may be 10 electrons moving around causing an ...
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1answer
57 views
Can I use time evolving block decimation (TEBD) to simulate the dynamics for many body localized systems?
In the many-body localized phase, the system is described by quasi-local integrals of motion ("l-bits"). The entanglement does grow logarithmically with time. So if I use TEBD to get the real-time ...
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How to find many body states whose total $L_{z}$ eigen values are zero?
I am trying to solve construct matrix representation of Helium atom. The hamiltonian is ,
$$H=-\frac{1}{2}\sum_{i=1}^{2}\nabla^{2}_{i}-\sum_{i=1}^{2}\frac{2}{r_{i}}+\frac{2}{|\vec{r_{1}}-\vec{r_2}|}$$
...
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What is motivation behind understanding many body localization?
I'm reading about many body localization which consider both interaction and disorder. But I don't know why this topic has gained so much attention? What is harder part of this localization that makes ...
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42 views
Reduced density matrix of two spins
I am reading this (https://arxiv.org/abs/1209.0062) article about constructing order parameters from reduced density matrix. The author is discussing long-range order by taking antiferromagnetic spin ...
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Can choose the following basis to solve hydrogen molecule?
I am trying to solve the problem of two proton and two electron problem, treating electrons quantum mechanically and ignoring the electron electron repulsion. The electronic Hamiltonian is as follows,
...
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1answer
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Hartree-Fock approximation
The Hartree-Fock approximation is used in solving many-body quantum mechanical systems. The problems of these type of systems are the e-e repulsion term in the Hamiltonian and the single electron ...
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3answers
153 views
Why bosonic field operator in momentum space contains both creation and destruction operator?
For fermionic field, the transformation from real space to momemtum space is a simple Fourier transformation $$\psi^\dagger(x)=\sum_{\mathbf{k}}c^\dagger_{\mathbf{k}}e^{ik\cdot x}$$ But in bosonic ...
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1answer
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Where are the poles of the one-particle Green's function located in the complex plane?
This post is a followup question to: How to get an imaginary self energy?
In the cited post, the two following representations for the one-particle Green's function are shown:
$$G(k,\omega) = \...
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Majorana Fermion Coherent States
I was wondering if there are coherent states for Majorana operators, so, states that fulfill the relation
\begin{align}
\hat{\gamma}_A |a,b\rangle &= a |a,b\rangle \\
\hat{\gamma}_B |a,b\...
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0answers
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How self consistency condition works for a superconductors which is finite and does not have periodic boundary condutions?
So if a superconducting system has periodic boundary conditions the s wave superconducting order parameter calculation by self consistency condition is pretty straightforward.
However what if I have ...
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Procedure for Effective Hamiltonian using Perturbation Theory? (Bilayer Graphene model)
Sorry if this is a dumb question as I'm just starting out, but in this paper https://arxiv.org/pdf/1803.08057.pdf on Twisted Bilayer Graphene, the authors claim to use "standard perturbation theory" ...
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Why can't the Schrödinger equation be solved exactly for multi-electron atoms? Does some solution exist even in principle? [duplicate]
NOT a duplictae, see EDIT below
It is common knowledge that the Schrödinger equation can be solved exactly only for the simplest of systems - such the so-called toy models (particle in a box, etc), ...
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What is an intuitive explanation of wave ordering vector $Q$? (Pierls Instability)
How does the wave ordering vector $Q$ order a CDW? I saw this vector while studying the following system.
We have a system with $N$ sites and $N/2$ spinless fermions and system is in the fully ...
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31 views
Variational wave functions in many-body physics
One of the very famous variational wave functions is Gutzwiller wave function (GWF) which explained Mott-insulator transition back in 60s/70s. It is analoguous to the idea of Projector Monte Carlo ...
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1answer
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Could you use the Barnes-Hut algorithm iteratively— with multiple center quadrants?
I was wondering if you could use Barnes-Hut simulation beyond what it was originally intended to be. For many Barnes-Hut algorithms, the forces are only considered for a single quadrant, the centroid, ...
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1answer
70 views
How does projector Monte Carlo method work?
Projector Monte Carlo states that if we have a trial wavefunction $|\phi\rangle$ which is not orthogonal to true ground-state $|\psi\rangle$ of the system then application of a projector
$$P=\exp{(-\...
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Proof of factorization at late times for chaotic systems
While reading the paper "A bound on Chaos - Maldacena et. al", https://arxiv.org/abs/1503.01409 in equation (23) of the paper they factorize a correlator of the form,
$$ Tr [\rho^{1/2} W(t) V \rho^{1/...
