The study of physical properties condensed phases of matter, including solids and liquids.

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Neutralizing Background and Fractional Quantum Hall ground state

The idealized many-body Hamiltonian describing FQH is given by $$ H = \sum_i \left\{\frac{[\vec{p}_i -e/c \vec{A}(\vec{r}_i)]^2}{2m}+V(\vec{r}_i)\right\} + \frac{1}{2}\sum_{i\neq j} ...
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42 views

Effective mass approximation Wannier function lattice vector operator approximate representation proof. Yu and Cardona

I am having difficulty in Yu and Cardona 4th edition chapter 4 page 164, equation 4.9 to 4.10 I just do not understand how to go from line 4.9 to 4.10. 4.9: $$ R_{op} \psi(\mathbf{r}) = ...
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87 views

Number Conserving Superconductors

Usual BCS theory used to describe superconductors violates particle number conservation, this is allowed since that theory is written in a grand canonical ensemble (i.e particles can be exchanges ...
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35 views

Why is graphene “gate tunable”?

I am reading Geim and Novoselov's classic paper on electrostatic doping of graphene: http://arxiv.org/abs/cond-mat/0410550 Three parts to the same broad question: 1) I am looking for some rigorous ...
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31 views

What is the 'dimensionality' in solid state materials?

In the context of condensed matter physics, when it is referred to a '1D', '2D' or '3D' material, what context is this dimensionality understood in? Real space? momentum space? or something else? We ...
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42 views

Static structure function for non-interacting Fermi gas

I'm wondering how would one go on about to calculate the static structure function with the ground state being $|\phi_0\rangle$: $S_\vec{q}=\frac{1}{N}\langle ...
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49 views

Inuitive analogy for localization?

I'm looking for a plain English analogy for electron/wave localization. And in particular weak localization and Anderson/strong localization. Is it possible to describe these phenomena in simple terms ...
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63 views

Correspondence between variational method and Feynman diagrams

There are two ways to look at the Hartree or Hartree-Fock equations. One method relies on the variational method for a particular type of the probe function and the second one originates from ...
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246 views

Perturbative series for bosons

I have recently read that ... the perturbation series ... is valid only when the perturbed state is qualitatively similar to (or ‘has the same symmetry as’) the unperturbed state. This means ...
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101 views

Can mercury evaporate if it's covered by water?

I was recently watching a video about elemental mercury and how it's cleaned up in water (fish tanks), and it was mentioned how mercury can be toxic in vapor form. My question is, if I were to drop a ...
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33 views

Can magnetization measurement give dimensionless susceptibility without knowledge of volume and density of the material

In a magnetization measurement (as a function of temperature) experiment, M is measured in emu (1 emu = 1 erg/G). Weight of the sample used in the experiment is known. Without knowing the volume and ...
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37 views

Nuclear Cusp Condition

Suppose I write a Hamiltonian for an atom, it will contain electron-electron repulsion term and nucleus-electron attraction term. But, these terms will diverge, for example, position of an electron ...
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76 views

What makes a system topological?

As I understand, if the Chern number which is obtained by integrating Berry curvature over a surface with a boundary is an integer, then the Chern number is a topological invariant. So when does Chern ...
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73 views

What's phonon mean free path

This is probably a naive question but still. Phonons are quasiparticles that emerge when we quantize motion of a lattice. In this sense, they have no location in space, they are just energy quanta of ...
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57 views

Hubbard model in the t>>U limit

I know one can obtain the t-J model from the Hubbard one by taking the limit $t\ll U$ in the following Hamiltonian: $H= -t\sum_{i\neq j}a_{i\sigma}^\dagger a_{j\sigma}+U\sum_i ...
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77 views

Ground state of AKLT chain invariant under time-reversal?

The AKLT chain is an example of an SPT phase protected by time-reversal symmetry. The Hamiltonian of the system has time-reversal symmetry. The ground state wave function can be pictured as follows ...
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65 views

Wavefunction for Anti-Pfaffian state

What is the most general form of a wavefunction for anti-Pfaffian in variables $\{z_i\}$ which represent the positions of electrons on a two dimensional plane?
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60 views

String operator in the string-net model

The string operator is a way to study the quasiparticle excitations in the string-net model http://arxiv.org/abs/cond-mat/0404617. It is claimed in the above reference (Eq.(19), p.9) that for string ...
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why are quantum vortices so large?

Quantum vortices in helium are almost macroscopic, and can be be imaged in a light microscope: http://www.aps.org/units/dfd/pressroom/papers/gaff09.cfm How can vorticity be quantized on such a large ...
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Hamiltonian in Majorana basis

I read (for example here: cond-mat/0010440) very often that if we transform the Hamiltonian from a fermionic basis to the basis of Majorana operators by expanding the fermionic operators in real and ...
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41 views

Underdoped Cuprates

What does underdoped cuprates mean? I guess cuprate is underdoped when hole concentration is less then optimal doping. Am I Right?. or it is something difference?
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97 views

How to do continuum approximation?

Assume you have $N$ matrix fields $T_{j}$ on a 1d lattice with lattice constant unity. Now consider a sum like the following (you can think of the traces as supertraces), and subject it to a continuum ...
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57 views

Landau level for quadratic band touching in Dirac Hamiltonian

I wonder if there is anyone or any references that have solved the Landau level spectrum and eigenstates with respect to the following Hamiltonian: \begin{equation} ...
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84 views

Where can I get an introduction to the mathematics behind Hofstadter's Butterfly?

Are there any good books that give good mathematical/physical background to the workings of the Hofstadter's Butterfly? I'd appreciate some references. Books or Public access papers will work. ...
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389 views

What is a Dirac semimetal?

What is the precise definition of a Dirac semimetal? Is it sufficient for two bands to touch at a single k point with a linear crossing, or are more conditions required for a material to be called a ...
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94 views

6j symbols with Majorana indices

The Levin-Wen model is a Hamiltonian formulation of Turaev-Viro (2 + 1)d TQFTs. It can be constructed from a unitary fusion category $\mathcal{C}$, which can be equivalently defined using $6j$ ...
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128 views

Why can gold be drawn out finer than light?

The metal gold is extremely malleable. Gold is also ductile and one ounce can be drawn into 80 km (50 miles) of thin gold wire (5 microns diameter) to make electrical contacts and bonding wire. I ...
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508 views

Jet turbine blades from single crystals, how are they formed?

I know about nothing about crystals, although I do know a bit more about jet turbine engines, and I definitely know that you don't want the fan blade hitting the fan housing. The reason given in the ...
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135 views

Different electrons, why aren't they all the same?

Why do we say that there are different kinds of electrons when discussing different situations in physics? For instance the Weyl electron, Dirac electron etc. From my exceedingly basic knowledge isn't ...
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55 views

Why is there longitudinal conductance in a partially-filled Landau level?

Suppose I consider an infinite, non-interacting (so no FQHE should happen) 2DEG in the magnetic field $\vec B=B\hat z$ with a non-integer filling factor, say 0.13 or whatever. Suppose I apply an ...
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83 views

Would condensed matter physicists need more than three dimensional calculus? [closed]

The difference between "multivariable" and "vector" calculus, as stated on Yale's website, is that multivariable would only go through 2 or 3 dimensions, and so would rely heavily on geometric ...
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50 views

Reference request on condensed matter field theory including Classical Field Theory

I was hoping for a reference request for a book on basic/introductory condensed matter field theory. In addition to the usual topics I am looking for books with reference to classical physics ...
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32 views

What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...
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119 views

Why is the plaquette operator in the string-net model a projection operator?

In the string-net model, the plaquette operator is defined as $B_P = \sum_{s}a_s B_{P}^{s}$, where $s$ runs over the string types $\{0,1,2,\dots,n\}$. It is claimed on page 19 of ...
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61 views

Free phonon propagator in imaginary time

The free phonon propagator in Matsubara space is given by $$D^0(i\omega_n)=\frac{1}{M}\frac{1}{(i\omega_n)^2-\Omega^2}.$$ I want to derive its representation in imaginary time. I know the result ...
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40 views

Time-reversal transformation for two-component bosonic models

Consider a two-component bosonic model $\mathcal{H}=-t\sum_{i\sigma}{b_{i\sigma}b_{i+1\sigma}^\dagger}+h.c. +\sum_{i\sigma\sigma^\prime}U_{\sigma\sigma^\prime}n_{i\sigma}n_{i\sigma^\prime}$. Here ...
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114 views

What is a Fermi arc?

What is meant with a Fermi arc in the context of Weyl semimetals? Is this the just a one-dimensional Fermi surface? For example, in electron-doped graphene, the Fermi surface consists of 2 disjoint ...
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42 views

How to conserve energy with electrical noise?

If a resistor experiences thermal noise, it will dissipate energy to the environment. But where does the resistor's energy come from? It seems that it will just lose energy until ran out.
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100 views

Interpretation of negative mass in condensed matter physics

I am reading the book "Topological insulator: Dirac equation in condensed matters" by Shun-Qing Sheng. I do not know much about this topic and this is the first time I am confronted with it, so this ...
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34 views

about Conservation laws and Correlation function

I'm reading a review paper by Gorden Baym-(http://www.worldscientific.com/doi/abs/10.1142/9789812793812_0002) In the second part, he raised that: According to conservation law $\frac{\partial ...
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Why is there a band structure for strongly correlated systems?

The existence of band structure of a crystalline solid comes from the Bloch theorem, which relies on the independent-electron approximation. Why do people still talk about the band structure for a ...
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31 views

How can a phosphorous ion dope silicon when it is already ionized?

In ion implantation dopant ions are directly bombarded into the semiconductor (silicon for example)? But if say P ions (P+) were implanted then it does not have an extra electron to donate into the ...
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130 views

When do gauge theories have protected gapless excitations?

Goldstone's theorem states that a system in which a continuous symmetry is spontaneously broken necessarily has gapless excitations. (A hand-waving "proof" of Goldstone's theorem can be given by ...
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Holography with wave functionals rather than partition functions

Roughly speaking Gubser-Klebanov-Polyakov Witten's (GKPW) prescription in the context of holography tells us partition function of CFT is "equal" to that of the gravity theory in one higher dimension ...
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meaning of $k$ in $k\cdot p$ approximation in condensed matter physics

Sometimes, I encounter such a practice in condensed matter literature: One takes a $k\cdot p$ hamiltonian $H(k)$ and substitute $k$ for $\nabla_r$, and then he solves the equation: ...
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73 views

Second order pole in Feynman diagrams

Hi, I am calculating density-density correlation function for a homogeneous electron gas. The Green's function for one of three first order connected diagrams(see attached figure) is, $$ ...
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81 views

What is continuum limit (low energy limit) in condense matter physics?

In condensed matter theory, I can sometimes encounter such a term as continuum limit, also known as low energy limit. I have a question about this term, let me illustrate my question through an ...
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87 views

What is the physical meaning of an electronic system evolving adiabatically through a closed path?

I am trying to understand Physics behind the Weyl Fermion in Condensed Matter Systems. Electrons show Weyl fermionic behaviour in the vicinity of so called 'Diabolical Points' in the band structure. ...
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183 views

Self-teaching Green's function approach to quantum many-body systems

My question is where can I find a good book, review, online course, or all of them for self-teaching Green's function in quantum many-body problems (if it has problems with solutions for ...
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47 views

Why classical open system and Bose-Einstein condensate are not fundamentally the same?

The classical partition function for an open system is given as $$ Z_{\text{max}} = \sum_{N=0}^{\infty} \dfrac{h^{-N}}{N! } \prod_{j=1}^{N} \left( \sum_{i=0}^{\infty} e^{-\beta (E_{ij}-\mu)} g_{i} ...