Questions tagged [many-body]

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

950 questions
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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 formalisms, but lately, I've been seeing Keldysh more…
38
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2 answers

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 an elaboration by Kohmoto (1984), write the…
34
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2 answers

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 atoms in 2008. "Large atom number Bose-Einstein…
31
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5 answers

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 number of interdependent particles, why is solving…
30
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1 answer

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 Heisenberg model, we have Schwinger-fermion…
28
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1 answer

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? What is the relation between Anderson localization…
28
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4 answers

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 and insulators? Does it mean that the band gaps…
27
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7 answers

Why can't the Schrödinger equation be solved exactly for multi-electron atoms? Does some solution exist even in principle?

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), and the Hydrogen atoms; and not for relatively…
24
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1 answer

Does the Mott insulator exist?

The Mott insulator is a system that, due to strong electron-electron interactions, is an insulator but is expected to be a metal by formal charge counting of electrons in the unit cell. Often, the Mott insulator is defined to be the ground state of…
23
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2 answers

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-electron interactions and the constant term is…
23
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2 answers

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 system, $c_k$ is the overlap between…
Lagerbaer
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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, auxiliary fields are introduced via an integral…
leongz
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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, then finally one huge globular cluster like clump…
19
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4 answers

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 is spontaneously broken is the discrete…
tparker
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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 important in the thermodynamic limit, but since I am…
Chenfeng
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