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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43
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5answers
12k views

Good reading on the Keldysh formalism

I'd like some suggestions for good reading materials on the Keldysh formalism in the condensed matter physics community. I'm familiar with the imaginary time, coherent state, and path integral ...
31
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2answers
11k views

Kubo Formula for Quantum Hall Effect

I'm trying to understand the Kubo Formula for the electrical conductivity in the context of the Quantum Hall Effect. My problem is that several papers, for instance the famous TKNN (1982) paper, or ...
31
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1answer
1k views

What is the largest number of bosons placed in a BEC?

What is the record for the largest number of bosons placed in a Bose-Einstein condensate? What are the prospects for how high this might get in the future? EDIT: These guys reported 20 million ...
26
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5answers
7k views

What are the primary obstacles to solve the many-body problem in quantum mechanics?

(This is a simple question, with likely a rather involved answer.) What are the primary obstacles to solve the many-body problem in quantum mechanics? Specifically, if we have a Hamiltonian for a ...
25
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1answer
7k views

What is many body localization?

Is there any good definition of many body localization? It is the property of one state or it is the property of a Hamiltonian? Why does disorder play an important role in many body localization? ...
24
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1answer
5k views

What're the relations and differences between slave-fermion and slave-boson formalism?

As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example, For ...
20
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7answers
12k views

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), ...
20
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1answer
1k views

Do gravitational many-body systems fall apart eventually?

Imagine an $N$-body problem with lots of particles of identical mass (billions of them). I saw several simulations on the Internet, where the particles first form small clumps, then bigger clumps, ...
19
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2answers
3k views

Why do Fermi liquids have $T^2$ resistivity?

I have often read that metals that are Fermi liquids should have a resistivity that varies with temperature like $\rho(T) = \rho(0) + a T^2 $. I guess the $T^2$ part is the resistance due to electron-...
18
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2answers
6k views

What is the difference between the Balmer series of hydrogen and deuterium?

In my quantum mechanics textbook, it claims that the Balmer series between hydrogen and deuterium is different. However, I was under the impression that the Balmer series $$H_\alpha, H_\beta, H_\...
17
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3answers
4k views

Why does Density Functional Theory (DFT) underestimate bandgaps?

Density Functional Theory (DFT) is formulated to obtain ground state properties of atoms, molecules and condensed matter. However, why is DFT not able to predict the exact band gaps of semiconductors ...
17
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3answers
999 views

Is a phason a Goldstone mode?

Suppose we have a lattice system whose ground state is an incommensurate charge-density wave (CDW). Strictly speaking, this ground state does not have Goldstone modes because the only symmetry that ...
17
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2answers
3k views

Subtleties in the exact solution to the 1D quantum XY model, in particular the Bogoliubov transformation

I am writing programs to construct the spectra of models with known exact solutions, and soon noticed some subtleties that are not often mentioned in most references. These subtleties are not ...
15
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7answers
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Is it wrong to talk about wave functions of macroscopic bodies?

Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not? For example in the "Statistical Physics, Part I" by Landau & ...
15
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1answer
1k views

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q a_{k_1+...
14
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2answers
4k views

How to get an imaginary self energy?

The Lehman representation of the frequency-dependent single particle Green's function is $$G(k,\omega) = \sum_n \frac{|c_k|^2}{\omega - E_n + i\eta}$$ where $n$ enumerates all the eigenstates of the ...
13
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3answers
2k views

Validity of mean-field approximation

In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where $...
12
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1answer
3k views

Feshbach resonance in simple terms

I was reading up Feshbach resonances in cold atoms and I was unable to grasp the concept. I will tell you what I have understood. We consider two body scattering processes elastic as well as inelastic....
12
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2answers
409 views

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 ...
12
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2answers
2k views

Why is the distinction between Mott Insulators and Charge Transfer Insulators important?

Strongly-correlated metals often become insulators due to the repulsive Coulomb interaction, and the basic model here is the Mott-Hubbard Model: $$H=-t\sum(\hat{c}_{i,\sigma}^{\dagger}\hat{c}_{j,\...
12
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1answer
602 views

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 ...
12
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2answers
366 views

Combining two finite number fock spaces into one

Say I have two separate systems of identical Bosons, one with N Bosons the other with M. System one is described by a state $|\psi_1\rangle$ the other with $|\psi_2 \rangle$ which are expressed in a ...
11
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6answers
1k views

Tsunami dampening mechanisms

Encouraged by the zeitgeist let me ask the following: Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it ...
11
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1answer
3k views

BCS-BEC crossover

It would be really helpful if somebody could describe what does one mean by a BEC-BCS Crossover. I was going through articles available on the topic, but I was unable to grasp the gist of the topic.
11
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1answer
504 views

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 ...
11
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3answers
3k views

Book recommendations for second quantization

I am trying to familiarize myself with the ideas of second quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. ...
11
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2answers
4k views

Questions about the Dyson equation

I'm studying finite temperature many-body perturbation theory, and am trying to understand The Dyson equation. In particular, I'm using Mattuck - A guide to Feynman diagrams in the many body problem. ...
11
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1answer
850 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 ...
11
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1answer
283 views

time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
10
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1answer
446 views

Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system?

One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits $$ \delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr] = \...
10
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1answer
363 views

What physics is contained in vertex corrections?

If one looks at the interaction of light and a non-zero density of electrons, one can calculate the polarizability $\Pi(q,\omega)$ (which is the 00-th component of the dressed photon propagator). This ...
10
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4answers
648 views

Question on the stability of the solar system

One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful ...
10
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1answer
540 views

Why are symmetric quantum ground states cat states iff the ground-state manifold is degenerate?

The usual story of symmetry-breaking quantum phase transitions (I won't consider topological transitions here) goes like this: you have a Hamiltonian $H(g)$ describing an infinite system which depends ...
10
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1answer
385 views

Two interacting electrons in infinite square potential - is there a solution?

If one were to look at Schroedinger's equation for two interacting electrons in a one dimensional infinite square well, it would something like this: $$-\frac{\hbar^2}{2m}\partial^2_{x_1}\psi(x_1,x_2)...
9
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2answers
2k views

Hubbard-Stratonovich transformation and mean-field approximation

For an interacting quantum system, Hubbard-Stratonovich transformation and mean-field field approximation are methods often used to decouple interaction terms in the Hamiltonian. In the first method, ...
9
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4answers
565 views

The Physical Meaning of Projectors in Quantum Mechanics

Let $O$ be a single-particle observable for a system, and $|L\rangle$ and $|R\rangle$ two orthonormal eigenstates of $O$. You may imagine that the system consists in two photons, and $|L\rangle$ and $|...
9
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1answer
1k views

Why are periodic boundary conditions used for the derivation of phonons? [duplicate]

I am currently reading "Quantum Field Theory for the Gifted Amateur". In chapter 2 Phonons are introduced as solutions (in k-space) of a coupled harmonic oscillator. In real space the oscillator is ...
9
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2answers
1k views

Why do we use the anticommutation relation for particle-hole and chiral symmetries?

In physics we say that a quantity is conserved, if its operator commutes with Hamiltonian. For example, in condensed matter systems, when the momentum $k$ commutes with the Hamiltonian $H$ as $[H,k]=...
9
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1answer
267 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 \...
9
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1answer
488 views

Correlated three-particle Green Function

I know the relationship between normal and correlated two-particle Green Functions for fermions: $$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$ Also known as irreducible n-...
9
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0answers
139 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 ...
8
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2answers
5k views

What's the reasons to use time-ordering operator?

I have met the time ordering operator $T$ in many places, such as in the Dyson series $$U(t) = T\exp{\left(-\dfrac{i}{\hbar}\int_0^tdt'H(t')\right)},$$ or in the definition of single particle ...
8
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1answer
1k views

Second Quantization in Condensed Matter and Quantum Field Theory

There appears to be an apparent dichotomy between the interpretation of second quantized operators in condensed matter and quantum field theory proper. For example, if we look at Peskin and Schroeder, ...
8
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2answers
2k views

Equation of motion for the reduced density matrix

The equation of motion for the density matrix of a many body isolated quantum system is the von Neumann's equation: $\dot{\rho }(t)=i[\rho (t),H]$. How about the equation of motion for the reduced ...
8
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1answer
1k views

Velocity distribution in Plummer's models and others mass distributions

The Plummer's sphere is an model for the mass density in a globular cluster of stars. For an $N$-body simulation I have initialized the position of $N$ masses with a Monte-Carlo technique but cannot ...
8
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1answer
2k views

Many Body Physics: Hamiltonian block structure and Symmetries

Consider a many body problem of a small cluster, e.g. the 'Hubbard-Cluster' (albeit the question may be of relevance for other Hamiltonians as well): $$\mathcal{H}=\sum_{<ij>\sigma} t_{ij} (c^\...
8
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2answers
474 views

Confusion regarding field operators

Second quantisation of the scalar field leads to an algebra of quantum field operators $$ [\phi(x),\phi(y)] = 0, \ \ [\pi(x), \pi(y)] = 0, \ \ [\phi(x),\pi(y)] = i\hbar \delta(x-y). $$ Where the field ...
8
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3answers
366 views

Density of states in a system of interacting electrons

When we are introduced to the density of states in typical band-theory problems we neglect interaction between electrons, and thus we define the density of states of a sigle particle as: $D(E)=2\int_{...
8
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2answers
287 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|...
8
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0answers
59 views

Do correlations in local quantum spin systems always decay exponentially or algebraically?

Consider translation-invariant quantum spin systems, that is qu-d-its on a lattice with a geometrically local Hamiltonian. Usually, such models are either gapped (in an ordered/disordered phase) or ...

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