Questions tagged [condensed-matter]

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

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What form or state of matter is a black hole

Neutron stars form dense clusters of neutrons which I have heard being called an element 0 and theoretically could form strange matter and the like from what I have read. Given that a black hole is ...
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Help. In tight binding 2d square lattice with two atoms basis

How we get the equations inside the box, which represent hopping between p and d orbital. I mean why we consider only two neighbouring. Thanks in advance
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How to obtain hydrodynamics from many-body quantum mechanics?

It is known that the Schrodinger equation is equivalent to the Euler equation (with a "quantum potential" term) and to the probability conservation equation (which is formally identical to ...
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Conductance of an interacting quasi one dimensional wire using the method for a 1D Fermi gas?

Assuming the electrons are non interacting and spin degenerate, the conductance of a quasi one dimensional quantum wire is quantised in units of $2\frac{e^2}{h}$. For small voltages, we simply count ...
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What is the difference between Keithely model 2612 and 2612A

I'm looking to buy an additional Keithely for my setup. I've been looking at the Keithely 2612 and 2612A, but I was wondering what the difference between the two is. I've been looking in the datasheet,...
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When does the characteristic length deem a layer infinitely thin?

When reading Real-time terahertz imaging with a single-pixel detector a paragraph states: "(...) these carriers will diffuse inside the semiconductor with a characteristic length around ~ 0.3 mm ...
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Does one ever need infinitely many cohomologies?

In a theory containing gauge fields or higher-form gauge fields, if the background spacetime is a complicated manifold, a nice way to represent the configuration of the gauge field mathematically is ...
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How to convert absorption/emission rate of a molecule from cross section units (or molar extinction units) to frequency units?

I try to find relation how absorption/emission rate of molecules is expressed in different types of units? For example, I found that for Rhodamine 6G the peak absorption rate (in terms of molar ...
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Anderson's poor man's scaling for Kondo model

I computed these contributions: $J^+J^-\rho_0\delta D \left(\frac{1}{2}-S^z\right)c_{ k' \uparrow}^\dagger c_{ k \uparrow}\frac{1}{E-D+\epsilon_{ k}}$ $J^+J^-\rho_0\delta D \left(\frac{1}{2}+S^z\right)...
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Time reversal symmetry and quantum spin Hall effect

As it knows the edge states in QSHE are protected by TR symmetry, so any perturbation that are symmetric under time reversal cannot destroy these states. A key point is that for $T^{2}=-1$ we have a ...
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Effective one-particle hamiltonian from many-body Green function

Consider a many-body Green function in terms of localized orbitals, $G_{\mu \nu}(\omega).$ The underlying hamiltonian is something like (I will write it with a great generality and omitting spin, this ...
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How to understand the anti-ferromagnetic picture for Slater insulator?

The Mott insulator is "local" picture and comes from strong interaction. This means single electron stays at their own site, and results in anti-ferromagnetic(AFM) order via super-exchange ...
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Divergences in resolvent expansion of Anderson hamiltonian

I'm reading these lecture notes on Anderson localization, and I cannot understand how the resonant regions contribute to the divergence of the resolvent expansion (sections 3.1 and 3.2). The relevant ...
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Instantons in Altland/Simons

I have a question about a statement in Condensed Matter Field Theory (2nd edition) by Altland/Simons on p.124. In short, when we consider a motion in a double well we obtain a classical solution in ...
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Ambiguity of mean field approximation

I have a Condensed Matter Hamiltonian on some lattice (eg. square or triangular) \begin{equation} H = \sum_{i,j} :\hat{a}_j^\dagger \hat{a}_i \hat{a}_i^\dagger \hat{a}_j: = \sum_{i,j} \hat{a}_j^\...
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What's the relation between degeneracy and $\pi$-flux

Ring with magnetic flux Assuming a particle locates in a ring which circle a magnetic flux, the Hamiltonian is: $$\hat{H}=\frac{1}{2 m}(\hat{p}-A)^{2} \rightarrow \frac{1}{2 m}\left(-i \partial_{\phi}...
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Low temperature resistance of metal

Is there any intuitive explanation of why resistivity of metal goes as $T^5$ at low temperature? The Debye theory gives that the phonon distribution goes as $n(\omega)\sim T $ at higher temperature ...
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Calculating the residue as part of Matsubara summation

On page no. $166$ of "Many-body quantum theory in condensed matter physics" by Henrik Bruus & Karsten Flensberg, while explaining the summation of Matsubara frequency, the following ...
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A quadratic Hamiltonian is a model of independent particles - why?

I'm reading some notes on the Anderson Hamiltonian: $$ H=\sum h_i c_i^\dagger c_i -q\sum_{\langle i,j\rangle}(c_i^\dagger c_j+c_j^\dagger c_i)$$ Where the $c_i/c_i^\dagger$ are fermionic annihilation/...
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Books on Condensed Matter after reading Messiah's Quantum Mechanics

What are some good books on Condensed Matter physics that will be accessible after reading Messiah (both volumes)? With no prior background in Condensed Matter, and that explain concepts in an ...
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Where do interactions enter the composite fermion theory in the fractional quantum Hall effect?

The question is, in short, where in the composite fermion argument are electron-electron interactions used? I know that interactions, namely Coulomb repulsion, between electrons are crucial in ...
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If a quantum state occupied by an electron has a $m^*_e>0$, will the same state if unoccupied have $m_h^*<0$ and vice-versa?

For electrons in a periodic potential, the effective mass of an electron in an energy band can be positive or negative depending on its quantum state specified by $n,k$ i.e. its energy $E_n(k)$ and ...
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Deforming a nematic line defect to a uniform configuration

In Nakahara section 4.9, "Defects in nematic liquid crystals", it is discussed that the order parameter for a nematic should be the real projective plane $\mathbb{R}P^2$, which has ...
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55 views

Why does Einstein's theory of specific heat fail only at one extreme of temperature?

Why does Einstein's theory of specific heat of solids work well at high temperatures but fail at low temperatures?
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What precisely does competing order mean?

I often see the term "competing order" thrown around in papers. What precisely does this refer to? It seems that it has something to do phase transitions, but can anyone offer a precise ...
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Crystals and Earnshaw's theorem

Earnshaw's theorem states that there can be no stable equilibrium in an electrostatic field. Now consider an ion in a cubic lattice, eg, a sodium ion in NaCl. That ion is certainly in stable ...
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How does the Bloch sphere indicate topology of 2-level $k\cdot p$ effective Hamiltonians?

It is known that the topology of some parameter space of a 2-level system (such as the Brillouin torus) may be found via the Gauss map to the Bloch sphere. The topology is indicated by the number of ...
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Why Bose-Einstein condensate is superconducting

Im looking into Quantum Computing, where the BCS Theory is used to build Qubits with a BEC. Why does the Bose-Einstein Condensate not interact with other particles and hence has no dissipation? In ...
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DOS for anisotropic 2D electron gas dispersion

If we start with the simple 2D isotropic-parabolic dispersion, \begin{align} E\left(\textbf{p}\right) & \approx\tilde{\varepsilon}_{0}+\alpha p_{y}^{2}+\alpha p_{x}^{2}, \label{1} \end{align} ...
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Physical meaning of constant zero phonon dispersion relation

Consider a 2D lattice model like this Assuming the mass of atom and force constant is 1, we could easily calculate the dispersion relations of the system. As there are four atoms per unit cell, there ...
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63 views

How to transform a given Lagrangian to a Nambu-Gorkov basis?

With reference to the Nambu (or famously, Nambu-Gorkov) transformation in this paper, could someone explain the reason behind using the 3rd Pauli matrix in the Lagrangian after equation (2.3) (would ...
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High symmetry point formulas for energy bands in empirical tight binding

I have a question about some intriguing formulas that I found. I am following ...
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Reference for understanding vortex physics in superconductors

I have been trying to find a good reference to understand the motion of vortices in type-II superconductors. While most textbooks on superconductivity talk qualitatively about this subject, I have ...
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Symmetry for dipole conservation in field theory

In article The Fracton Gauge Principle complex scalar field is considered. There's statement, that for conservation of charge one needs usual U(1) global symmetry: $$ \phi \to e^{i\alpha}\phi \...
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The largest possible global symmetry of a 2-dimensional Hilbert space?

Suppose we have a quantum system of a 2-dimensional Hilbert space $\mathcal{H}$ and a Hamiltonian $\hat H$. My puzzle: What is the largest possible global symmetry for the Hilbert space $\mathcal{H}$ ...
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Retarded van der Waals force / Casimir Effect

So, I read that in the case of the nonretarded Van der Waals force, two atoms are at a separation distance, so that a virtual photon emitted by one atom cannot reach the other during its lifetime. At ...
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Wick's theorem for non-equilibrium steady state

I am working on a grand canonical Hamiltonian which has the form: $$ \hat{K}=\hat{H}_{SC}+\hat{H}_{tip}+\hat{H}_{T}-\mu\hat{N}_{SC}-(\mu+eV)\hat{N}_{tip} $$ where $\hat{H}_{T}=-t_0\sum_{\sigma}(c^{\...
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Lattice vibration and sound waves

In general, the acoustic branches of a crystalline solid has a nonlinear dispersion relation. For small values of the wavenumber $k$ or wavelengths large compared to the equilibrium lattice separation,...
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RKKY approximation regime of validity

The RKKY effective action applies 2nd order perturbation theory to the interaction of magnetic moments $\vec I_n$ with conduction electrons $$H_{eS}= \frac12 \frac{J}{V} \sum_{k,k'} \vec I_n e^{i(k-k')...
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In what sense is a magnon a particle with momentum $p$ moving in the groundstate?

(I realize this might be a more general question completely unrelated to magnons) To illustrate my question, consider the XXX Heisenberg model, $$ \mathcal{H}=\frac{J N}{4}-J \sum_{i} \left( \frac{1}{...
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Quantify/visualize atomic clusters in multi-component crystalline materials

Let's say we have a material $AB$. Is it possible to detect atomic clusters of A atoms experimentally? The size of clusters in question: 2 atoms (nearest neighbour (nn) pairs), 3 atoms (nn triangles), ...
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Electromagnetic field in the Casimir effect

So, I read, that the Casimir effect arises from the ground state of the electromagnetic field. But I don't understand where the electromagnetic field in the Casimir effect comes from, since we are ...
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What is topological in Kitaev Chain

What is topological in Kitaev Chain? Realspace or the space of Pauli spins or the space of fermions? My Understanding I understand that majorana-zero modes are which are spatially separated, are ...
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For finite magnetic field B, the exact ground state of transverse Ising model still does not break the 𝑆𝑧β†’βˆ’𝑆𝑧 symmetry

In the comments of OP What is spontaneous symmetry breaking in QUANTUM systems? There is a statement by OP Xiao-Gang Wen saying "the ground state of transverse Ising model $$𝐻=βˆ’βˆ‘π‘†π‘§_𝑖𝑆𝑧_𝑗+𝐡...
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About universal quantum computation by β€œquantum wires”?

In this paper: A. Y. Kitaev, "Unpaired Majorana fermions in quantum wires", Phys.-Usp. 44 131 (2001), arXiv:cond-mat/0010440, it says: Unlimited quantum computation is possible if errors in ...
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Why is $\sum_{i=0}^N S_i^z S_{i+1}^z |\uparrow … \downarrow_n … \uparrow \rangle = \frac{1}{4}(N-4)$?

I am following these (http://edu.itp.phys.ethz.ch/fs13/int/SpinChains.pdf) lecture notes and I can't understand why given the following XXX Heisenberg hamiltonian $$ \mathcal{H}=\frac{J N}{4}-J \sum_{...
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When/why does an evolving wavefunction loop intersect with itself?

Let's say I have a 2-state system described by a $2\times 2$ non-degenerate Hamiltonian in some 2D parameter space. This is in the context of condensed matter, but should be more fundamental quantum ...
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Flat-Band Basis (Bernevig & Hughes) for computation of Hall conductance

In Topological Insulators and Topological Superconductors (Bernevig & Hughes) a limit of an insulating Hamiltonian, the flat-band limit is used to compute the Hall conductance. For the fist we ...
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The anticommutator of two field operators

I am a bit confused on how to show that the two electron field operators anticommute as such, If the field operator $\Psi_{\sigma}(\hat{r})$ is defined as, $$ \Psi_{\sigma}(\hat{r}) = \sum_{\alpha} \...
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Analytically calculate the zero energy edge states of the Su-Schrieffer-Heeger model

Is it possible to analytically calculate (or verify the existence of) zero energy edge states for the SSH model in real space? This seems to be discussed in Section 1.5.2 of "A Short Course on ...

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