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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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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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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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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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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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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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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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conservation of Momentum in indirect bandgap materials

I'm not a physicist but worked with band structure, band manipulation during my graduate engineering work. I need someone with a better understanding of band structures and k vector to help break down ...
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1answer
42 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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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
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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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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
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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
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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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Why repulsion between adjacent levels disappear in Poisson distribution?

In Poisson distribution $P(s)= exp(-s)$ why when spacing s between two energy level is zero P(s) is 1 means there is maximum probability that two levels are close to each other. Can I say that ...
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Can we observe the cross over between different Dyson ensemble distributions at the same time?

In random matrix theory we randomly choose matrix elements But they should follow certain symmetry properties. According to Wigner there can be 3 distributions GOE,GUE,GSE and these distributions are ...
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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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Why states close in energy stay away from each other?

According to random matrix theory in the presence of strong disorder off diagonal elements are suppressed and the states close in energy reside far apart from each other. Why is is so?
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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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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
86 views

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
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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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In Poisson distribution probability is function of level spacing or mean level spacing?

In Poisson distribution $P(s)=\exp(-s)$, where $s$ is the spacing between two adjacent energy levels. But when I plot graph between $s$ vs $P(s)$ by considering $s$ as spacing between adjacent level I ...
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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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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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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
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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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0answers
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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/...
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What “transformations” did Abrikosov use in 1958 to get the famous $11-2\log{2}$ result in fermi-liquid theory?

How does one obtain the final integral expression in the appendix of Abrikosov and Khalatnikov's 1958 paper: $\ \ \ $ "Concerning a model for a non-ideal fermi gas" $\ \ \ $ ??? Below, in Bold, I ...
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Infrared cutoff in the Kramers-Kronig relation for the marginal Fermi liquid

I am going through Andre-Marie Tremblay's derivation of the real part of the self energy in his lecture notes on the many-body problem. On page 254, if we take the imaginary $\Sigma''(k,\,\omega)\sim \...
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Asymptotic relation of Green's function for diverging self energy

I am considering the derivation on pages 64 to 66 of Zagoskin's Quantum Theory of Many-Body Systems. They consider a Green's function in the Lehmann representation: $$ G(p,\,\omega)=(2\pi)^3 \sum_s \...
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Help with Correlation/Green's Function of Rotated Variables (Keldysh Rotation)

I'm working through this paper, and have encountered "a little algebra shows that...", yet I'm not familiar enough with the topic at hand to figure this out. Here is the paper: https://arxiv.org/abs/...
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The link between spin singlet and the emergent (heavy fermion) fermi liquid in Kondo physics

I have been trying to understand the Kondo physics. Based on Anderson model, at low temperature $T<T_\text{K}$, the local spin gets screened by the itinerant electrons with a formation of the spin ...
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1answer
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Rotational invariance of many particle (quantum system) system?

I am trying to prove pairwise coupled harmonically interacting (quantum) system of particles as rotationally invariant . $$H=\frac{1}{2}\sum_{j}p_{j}^2 +\frac{1}{2}k\sum_{i<k}(\vec{r_{i}}-\vec{r_{k}...
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Is the replacement $i\omega_n\rightarrow \omega+i\eta$ in Matsubara Green function valid?

In many-body theory we know that to find the retarded Green function in frequency space $G^R(\omega)$ we first find the Matsubara time-ordered Green function $\mathcal{G}(i\omega_n)$ and then replace $...