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Questions tagged [condensed-matter]

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

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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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What is the meaning of the gap energy in superconductor?

For superconductors the energy gap is a region of suppressed density of states around the Fermi energy, but I do not understand the meaning of this.
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Co-propagating fermions with tunneling

When we have coupled fermions with an opposite chirality, the existence of the tunneling term will effectively act as a mass term and opens up the gap. When we bosonize the theory this mass term ...
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25 views

Many Body Theory for Condensed Matte [on hold]

Where can I get authenticate video lecture on Many Body Theory for Condensed Matter( Some full series from some recognised institution)?
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An idea to model a one-dimensional thermometer?

Let's say I have a $1$-dimensional material with thermal expansion $\alpha$: $$ \alpha l_0 = \frac{\Delta l}{\Delta T}$$ where $l$ is the length of the system and $T$ is it's temperature. This is ...
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The one-dimensional chain of the two atomic molecules [on hold]

The one-dimensional chain of the two atomic molecules (with different masses, the distance between them a) is spaced 3a. Assuming a constant of the end of the chain, using the harmonic approximation ...
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19 views

Weyl semimetal lattice model with real hoppings only?

Is there any lattice model of Weyl semimetal with real hopping amplitudes only? I was trying to find such a simplest model with only two Weyl points. As far as I've tried or read in papers, no ...
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rectangular two-dimensional lattice [on hold]

Consider a rectangular two-dimensional lattice of dimensions a and b from atomic molecules (atoms with masses m1 on the junction of the column and at a distance c from the atoms of the square with ...
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Symmetry Protected Topological (SPT) phases of spin-1 chains

Let's consider this family of 1D spin-1 of hamiltonians: $$\sum_{i}[S^x_{i}S^{x}_{i+1}+S^y_{i}S^{y}_{i+1}+\lambda S^z_{i}S^{z}_{i+1} + D(S^{z}_{i})^2].$$ If I understand it right, these models have: ...
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1answer
31 views

$C_4$ symmetry of Chern insulator

I was reading a paper that claimed the following Hamiltonian had $C_4$ rotational symmetry, $$ \hat{H} = \sum_{k} c^\dagger_k h_s(\bf{k}) \sigma_s c_k$$ where the Bloch hamiltonian is given by \...
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Is 2D toric code dual to something?

I can understand 2D toric code as a quantum Z2 gauge theory defined on a lattice. Is this model dual to some simpler spin model? A bit of motivation to clarify my intention: I know 3D classical Ising ...
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Landau free energy for an electronic nematic phase on a triangular lattice

I'm trying to write down the landau free energy for a nematic phase on a triangular lattice where I just take the order parameter to be a phenomenological scalar parameter indicating the degree of ...
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28 views

Calculation of density of states near a saddle point

I am trying to calculate density of states near a saddel point, where $$E(k) = E_c + \frac{\hbar^2}{2}\left( \frac{k_x^2}{m_x}+\frac{k_y^2}{m_y}- \frac{k_z^2}{m_z} \right)$$ Where, $E_c$ is the energy ...
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Significance of geodesics of a Hamiltonian surface in condensed matter physics?

Many Hamiltonians in 2D quantum systems can be parameterized as a surface (such as the Bloch sphere) by their k-space coordinates. Another example is given by the (kx,ky) points of the Brillouin torus ...
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Why does E-field decay in direction perpendicular to surface plasmons?

Ref: Surface Plasmons on Smooth and Rough Surfaces and on Gratings (by Heinz Raether), page 4 The setup described here is essentially depicted above. The field is described by $E=E_0^{\pm}exp[+i(...
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Inelastic collisions in molecular dynamics governing Boltzmann equation

In Huang's book on Statistical mechanics, the derivation of Boltzmann equation for a dilute classical gas assumes the molecular dynamics to be governed by two-body elastic collisions. As a consequence,...
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31 views

Operator to find position of a particle in many body system

I am reading the following article by Raffaele Resta about modern theory of polarization The quantum-mechanical position operator and the polarization problem My question is not about polarization....
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Calculating magnetic field outside the core magnetic field region (split pair superconducting magnet)

In this article, they have calculated fringe field from a split-pair magnet. It seems like the magnetic field strength is decaying exponentially. Which equation would support this kind of decay? ...
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Possible ground state wavefunctions of anti-ferromagnetic Heisenberg spin chains

What are the ground state wavefunctions of the anti-ferromagnetic (AFM) Heisenberg spin chains? Is that which of the following? $$| ↑↓↑↓ · · · ↑↓>$$ or $$| ↓↑↓↑ . . . ↓↑>$$ or $$| ↑↓↑↓ · · · ↑↓...
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What is the topological data for $(\mathbb Z_n)_p$ theories?

Consider the 3d TQFT described by the Lagrangian (Dijkgraaf-Witten with gauge group $\mathbb Z_n$ at level $p$): $$ \mathcal L=\frac{n}{2\pi} B\wedge\mathrm dA+\frac{p}{4\pi}A\wedge\mathrm dA $$ with $...
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Left and Right Eigenvectors of Transfer Matrix in Matrix Product States (MPS)

Let $\lvert{\psi}\rangle=\sum_{i_1i_2...i_n}Tr(A^{[1]}_{i_1}A^{[2]}_{i_2}...A^{[n]}_{i_n})\lvert{i_1 i_2...i_n}\rangle$ be a MPS, where $i_k=1,2...d$ and $A^{[k]}_{i_k}$ are $D\times D$ matrices ...
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What are phonon frequencies in solids? How are they related to the interaction potentials between the constituent atoms?

I was reading a paper on self-assembly of colloidal structures, where it was mentioned that only solids with real phonon frequencies are mechanically stable. And the authors go on to manipulate the ...
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1answer
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Diatomic chain and speed of sound

I have been unable to obtain the speed of sound in a one dimensional diatomic chain. Suppose you have a diatomic chain with particles of mass $M$ and others of mass $m$. The particles of the same type ...
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Deriving Chern-Simons term from path integral representation of the first quantized non interacting many body Hamiltonian

This is an exercise from condensed matter filed theory book of altland and simons. Exercise Subject the first quantized many particle hamiltonian $H=\sum_{i=1}^{N}\frac{p^{i}{^{2}}}{2m}+V(x^i)$ to ...
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Why does the hybridization occur between the orbitals that are even under a certain symmetry operations?

For example, in monolayers MoS$_2$, considering the prismatic coordination of the metal atom, the $d$-orbitals split into three categories: {$d_{z^2}$} {$d_{xy}, d_{x^2-y^2}$} {$d_{xz},d_{yz}$}. ...
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Gauss's Law about excess charge on conductors, quantum mechanics, and doped semi-conductors

Does quantum mechanics predict that there is any probability of finding excess charge inside a conductor? I've read an explanation about the distribution of excess charge placed on conductors. The ...
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56 views

What is finite size scaling theory?

The question is in the title. I read some articles about it but I could not understand it completely. What does it mean when we say scaling of any system? Can you please give a brief introduction ...
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22 views

Proof of the $U\left(1\right) \times SU\left(2\right)_{S} \times SO\left(3\right)_{O }$ symmetry of the Hubbard model

I want to prove the rotational invariance symmetry $SO\left(3\right)$ of the interaction term of the Hubbard Hamiltonian, which in general is \begin{equation} \hat{H}= U \sum_{m} \hat{n}_{m\uparrow} \...
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1answer
28 views

Electron correlation - difference between correlation and dependence

When we talk about electron correlation in condensed matter physics or chemical physics, we usually refer to the fact that the pair-density $$ P(r,r') = N(N-1) \int |\psi(r,r',r_3,...,r_N)|^2 \; \...
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1answer
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Experimental confirmation of Majorana modes in Kitaev chain

I'm confused about majorana modes at the edge of Kitaev chain, what do we seek in experiment? When we first define this one we write the creation and annihilation operators as: $$a^{+}=\frac{1}{2}(\...
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1answer
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Attempt at proving $-i\ \langle{u_n|\nabla_k u_n}\rangle=-\dfrac{i}{2}tr[v^\dagger(k)\nabla_k v(k) ]$ from Kane and Fu's paper

I am trying to prove result (3.4) of the following paper: http://li.mit.edu/S/2d/Paper/Fu07Kane.pdf namely, that $$-i\ \langle{u_n|\nabla_k u_n}\rangle=-\dfrac{i}{2}tr[v^\dagger(k)\nabla_k v(k) ]$$ ...
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Why we can not observe phase transition in finite systems? [duplicate]

In condense matter physics books it is mentioned that we can not observe phase transition in finite systems. Why is it so?
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3answers
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How fast can a “heat front” propagate through a material?

Say I have some piece of material (geometry at least I don't think should matter) that is at a uniform temperature. It then is heated (say, by an incident laser beam or something) at one spot, with a ...
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1answer
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Is the classification of (Symetry Protected) Topological Order for 3 band models different than for two band models?

I was reading this article: https://arxiv.org/abs/1512.08882 on the 10 fold way which gives a nice explanation of the possible topological phases for each of the symmetry classes. The example ...
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Why is the current in the nonrelativistic Dirac sea infinite?

Consider the model of a nonrelativistic noninteracting Dirac sea. I define the model as one with two infinite bands of single particle states: $$E_\pm (k) = \pm \biggr(\Delta + \frac{k^2}{2m}\biggr)$...
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What is the Bogoliubov transformation matrix for Fermions?

Is there any Bogoliubov transformation matrix for the operator $O=|g\rangle\langle e|$ where $|e\rangle$ and $|g\rangle$ are arbitrary states? I know that, for annihilation and creation operator $a$ ...
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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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1answer
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Points of symmetry in $k$-space

Can you relate a point in the reciprocal space with a vector in real space? How do I find the family of planes that represent a point of symmetry in the Brillouin zone? For example, germanium has ...
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Scale-free networks and phase transitions

When we say that networks can be scale-free, does that mean the same thing as "scale-free" when we talk about phase transitions or critical phenomena? I can tell they are similar insofar as they both ...
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1answer
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What is quantum fluctuation in the Bose-Einstein condensates theory?

I would like to understand what quantum fluctuation really means. I think it's the particles that are not in the ground state. Am I right? But then, what are the differences between quantum ...
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2answers
42 views

How is the a Fermi surface different from a Fermi sphere?

How is a Fermi surface (a surface in reciprocal space separating the occupied electron states from unoccupied states at $T=0$) different from a Fermi sphere? Is Fermi sphere a special case of Fermi ...
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1answer
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What is the difference between non-equilibrium and equilibrium phase transitions?

My question is about the distinction between certain kinds of phase transitions. I understand what the difference between first and second order ones are. What is the difference between non ...
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What is the link between superfluids and BEC?

i’m studying superfluids (in particular $^4 He$) and one of the first theorical apporoach was with Bose-Einstein condensation and i know that we can calculate the $T_c$ and it is close to the the ...
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1answer
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In a class of parametrized symmetric Hamiltonians, should its symmetry operator be parametrized the same way?

I would like to ask the following in the context of symmetry-protected topological phase. Consider a class of Hamiltonians parametrized by $\{a_1,a_2,...\}$ denoted by $H(a_1,a_2,...)$. Suppose there ...
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1answer
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Specifying the initial nonequilibrium distribution $f(\textbf{r},\textbf{v},t)$ in Boltzmann equation?

Within the single relaxation time approximation, the collision term in the Boltzmann equation is approximated as $$\Big(\frac{\partial f}{\partial t}\Big)_{\rm coll}=-\frac{(f-f_{\rm eq})}{\tau}$$ ...
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1answer
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Interface between two phases minima of the energy and interface between a minimum and a “vacuum”

Cahn and Hilliard define the energy of an interface: the difference per unit area of interface between the actual free energy of the system and that which it would have if the properties of ...
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2D diffraction pattern: Benzene (hexagon)

I am currently looking at 2D diffraction pattern. For starters I read: https://www.doitpoms.ac.uk/tlplib/diffraction/diffraction3.php When I have N=6 atomic scatteres in 1D just in a line, it will ...
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Fraunhofer's multiple slits versus atomic scatteres (diffraction)

I am currently busy with studying solid state physics and looking at diffraction theory. http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c3 explains Frauenhofer diffraction good. Let'...
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Obtaining real-space correlations from reciprocal space correlations

Consider a system of Ising variable $s = \pm 1$ on a rectangular lattice which has open boundary conditions on the top and bottom and periodic boundary conditions to the left and right. In other words,...
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Different Creation/Annihilation operators for neighbouring sites in Tight-binding model of Graphene

The treatments that I have seen of Graphene's Band structure assume an overlaying of two inequivalent lattices. However, can the reason for choosing different annihilation and creation operators (such ...