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0

May I also suggest "A Guide to Feynman Diagrams in the Many Body Problem" by Richard Mattuck, as a supplement to Altland and Simons, and Fetter and Walecka.


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Well, for strongly correlated systems, there are many other books you should read. E.g. for quantum order beyond Landau-Ginzburg's theory, Xiao-gang Wen's book is good:《Quantum field theory of many-body systems》. In this book, the path integral method is widely used and many materials not covered in other book are treated. Also, the chapter on quantum Hall ...


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V2O3 may be the material, which can be described by the pure Hubbard model. For CuO2, t-J model or even the Emery's three band model may be a more appropriate starting point as can be seen from optical experiments.


1

Well, there have several papers on this issue, e.g. PRB 86 4526. I have also studied this Hamiltonian in my paper arXiv:1410.6261. In my opinion, the RVB pairing induces the pairing of conduction electrons via the nonvanishing Kondo screening. To my surprise, such SC state is able to fit the experimental data of the heavy fermion superconductor CeCoIn5.[The ...


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Depending on what is shown in the band diagram, you can see if it's a topological insulator. Most band diagrams just show what's going on in the bulk material -- what you'd get with an infinitely large chunk of material with not surface. However, to be a topological insulator, you need surface states that conduct. These can be (and sometimes are) drawn on ...


0

You can see, where the band maxima and monima are and thus see, which gap is direct or indirect. In the case of a direct semiconductor, the CB minimum would be straight above the VB maximum. Bonding can not be seen directly, I think. But from the position of the Fermi level, you would see, if a material is behaving like a semiconductor or metallic. A ...


1

In quantum chemistry two-center integrals refer to exchange or coulomb integrals involving 1-electron atomic wave functions (orbitals) centered on two different atoms in a molecule. Say the coulomb repulsion between an electron described by an orbital belonging to atom A and another electron described by orbital belonging to atom B is given in a simplified ...


1

The answer lies in the fact that, in graphene, there is an effective long range interaction mediated by the inverse biharmonic operator (which in 2D goes as $x^2\ln(x)$ and is extremely long-ranged) coupling the gaussian curvature at any two points on the sheet. Due to this, any static ripples or thermally produced dynamic ripples interact at arbitrary ...


-1

Yes. Given any Hamiltonian $H'$, let $C_1=1$ be the identity operator and $h_{11}:=H'$ be a $1\times 1$-matrix. (If you want to have $h$ take values in a field, the fact that you propose a discrete sum over states will be insufficient if the Hamiltonian involves operators with a continuous spectrum like the standard momentum operator. I see you also leave ...


2

Then, there is the case that such an operator is defined on the full interval I assume that by "full interval" you mean the whole real line. First question: Do we then need any boundary conditions? Yes, as noted by Sam Bader, boundary conditions are part of the Hamiltonian. In my physics lecture we used so-called Born von Karmann boundary ...


4

What are phonons? Phonons aren't particles like electrons or protons are, phonons are quasi particles, these type of particles are just used to describe excitations of a field: in phonons case, phonons are used to describe elementary lattice vibrations which have certain frequency. Electron-Phonon Interaction: Basically Cooper pairs are just pairs of ...


0

I can answer you what is coherence length. Consider the Mach-Zender interferometer. A single particle wave-packet is split at a beam-splitter ($BS_1$) into two wave-packets, one transmitted and one reflected. Well, each wave-packet is brought, by reflecting it with mirrors, to a second beam-splitter ($BS_2$). Say, the reflected wave-packet from $BS_1$ ...


1

It's good that you're considering questions like this; I find that this type of questions really forces a student to a deeper understanding of the math involved. Do we then need any boundary conditions? Yes, boundary conditions should be considered as part of the definition of the Hamiltonian and its domain. Different boundary conditions can result in ...


4

any eigenfunction to this Schrödinger operator is automatically periodic with the potential's period, is this true? No!! The eigenfunctions are Bloch waves $\psi(x) = u(x)e^{ikx}$, where $u$ is periodic (with the period of the lattice). But the product $\psi$ is not periodic (with the period of the lattice) unless $k=0$. I put up an example on Wikipedia ...


4

Introduction: Superconductivity is phenomenon when certain materials electrical resistance drops sharply to zero when their temperature is lowered below it's critical temperature ($T_c$), There are two types of superconductors $\mathrm{Type\text{ }I}$ and $\mathrm{Type\text{ }II}$. Type I Superconductors: In $\mathrm{Type\text{ }I}$ superconductors ...


0

the Dirac Point on Graphene is protected by hidden symmetry. And it is explained very well in the paper arXiv:1406.3800. It is not that easy to understand the hidden symmetry. Personally speaking, I thought it is combination of inversion, time reversal and reflection symmetry, though the hidden symmetry in that paper has a totally different form with my ...


1

Equation 12 is $H' = -\frac{e}{i \omega m} \mathcal{E}_- P_+ e^{i\omega t}$, where $\mathcal{E}_-$ is the strength of the AC electric field $\omega$ is its frequency, $m$ is the electron mass, $e$ is its charge, and the other quantities are defined in the text. Plugging in the definitions, we find \begin{equation} \begin{aligned} H' &= \frac{ie}{\omega ...


8

The short answer is that BCS theory is derived bottom-up from quantum mechanics (you assume that there is some local attractive interaction between electrons, and perform a mean field approximation), while the older Ginzburg-Landau theory is derived top-down from thermodynamics (you assume that superconductivity can be described by some order parameter, and ...


1

Consider the partition function $$Z = \int D\phi ~ e^{-S_0 - S_I},$$ where $S_0$ is the Gaussian/free part and $S_I$ is the interaction part of the action. Within a perturbative framework we may aim to systematically include the contributions of fast modes to the (effective) action for slow modes. For this we expand in the interaction strength as $$Z = \int ...


0

The exciton is a quasi-particle. It can be thought of just the interaction energy between the hole and electron. This pair of particles obeys the Coulomb field and is a bound state. Much like the hydrogenic bound states, the exciton's energy is quantized through discrete levels. I suppose in the context of a many-body system, a hole will have local ...


0

Even if it's not really appropriate to derivate quantitative results about electrons properties in solids, Jellium model still have some interesting qualitative features. As you correctly pointed, Jellium still a mean-field theory and so fails about dealing with strongly correlated systems. Lets remind a few about jellium model. The starting point is the ...


1

This is certainly unexpected, for as Mark Mitchison commented the $J=0$ Heisenberg model is equivalent to free fermions in one dimension. Moreover I suspect that something is amiss even before that, for the $J=-1$ is the ferromagnetic model and $J=+1$ the antifferomagnetic one, and certainly they have different ground state energies. In fact, for $J\leq -1$ ...


2

Both! The fundamental physics comes from the fact that these were the first systems (in the pre-graphene era) to really exhibit two-dimensionality! In two dimensions, physics can be fundamentally different which is exhibited by the integer and fractional quantum hall effects, the quantum spin hall effect and Kosterlitz-Thouless-type phase transitions just to ...


1

Yes 2DEG offers some fundamental physics by eliminating one spatial degree of freedom. Of most important physics the quantum Hall measurement comes to mind. From a technological perspective, the bandgap engineering of heterostructure devices allows the formation of 2DEG, i.e. a high concentration of charge without recourse to mechanisms such as doping, ...



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