Anyon
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1 answers
19 votes
1k views
Is the number of possible Bravais lattices a mathematical fact?
22 votes

Quasicrystals were known well before 2015. The recent developments is in showing that such crystals exist naturally, rather than just in synthesized samples. The first (nowadays generally accepted) ...

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3 answers
18 votes
758 views
Ising model: How can I spot the critical point?
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17 votes

My question is, when I run a simulation with $N$ particles and I track the Hamiltonian per particle $(H/N)$ and the magnetization per particle $\left(\sum _i s_i /N\right)$, with $K$ values going from ...

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14 answers
42 votes
6k views
Supercomputers around the world
17 votes

USA: Facilities funded by DOE For USA, XSEDE was mentioned in [another answer](https://mattermodeling.stackexchange.com/a/1517/671). It is funded by the US National Science Foundation. There are also ...

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2 answers
18 votes
436 views
What are good random number generators for Monte Carlo calculations?
14 votes

It's been years since I've done Monte Carlo calculations (though it was more recent than the 90's!), so hopefully the information given below is still reasonably up-to-date. I've also had reason to ...

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1 answers
16 votes
265 views
The Hund's J - Why can this be quantified?
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12 votes

When I first read your question, I found it somewhat puzzling. I have to admit, I still do in part. Why? Well, even your link defines $J$ as a sum of matrix elements $\langle m,m'|V_{ee}|m',m\rangle$. ...

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1 answers
13 votes
341 views
Is Heisenberg model or in its simplier form Ising model a good approximation to study magnetic systems?
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12 votes

Introduction Your question reminds me of a quote by Paul Dirac, The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus ...

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2 answers
16 votes
430 views
Software for solving quantum systems in 1D and 2D
11 votes

Note: This answer was written when the question was specifically about exact diagonalization codes. In an ED context, "a large number of spin sites" would maybe mean somewhere in the 24-40 ...

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2 answers
11 votes
1k views
Is there any specific name for non-ferrous metals which are not noble metals?
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11 votes

I don't think it's ideal, but there is the term "base metal". There are various definitions for what is considered a base metal, but the main noble (or precious) metals are always excluded. ...

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1 answers
10 votes
300 views
What's the past and future of 2D materials since graphene?
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10 votes

Actually, if you allow for quasi-2D systems, graphene has had a recent renaissance starting with the experimental discovery of correlated states in "magic angle" twisted bilayer graphene, ...

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3 answers
20 votes
1k views
Introduction to protein folding for mathematicians
10 votes

Someone more familiar with the problem might have a better suggestion, but I recently came across Daniel B. Dix' notes on Mathematical Models of Protein Folding. This is not my field, so I won't ...

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2 answers
21 votes
510 views
Derivation of Slater-Koster equations
10 votes

Spherical harmonics are not themselves full atomic orbitals. Consider the Hydrogen wave function, which separates into a radial part and an angular part. The latter is a spherical harmonic, but the ...

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1 answers
11 votes
249 views
Anomalous Quantum Hall Effect
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10 votes

What is the quantum anomalous Hall effect? Figure from C-X. Liu, S-C. Zhang, and X-L. Qi. "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter ...

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2 answers
20 votes
278 views
What are the great unsolved questions in Matter Modeling?
10 votes

High-temperature superconductivity Superconductivity is a fascinating macroscopic quantum phenomenon in which, as some material is cooled below a critical temperature, its electrical resistance ...

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1 answers
9 votes
306 views
Proper handling of change of units in numerical calculations
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9 votes

You're correct, but there's also an easier way. I tend to rephrase such problems in terms of an overall energy scale and a ratio, e.g. $$ H=J\left[ \sum \limits_{\langle i,j \rangle} \vec S_i \cdot \...

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2 answers
19 votes
448 views
What is a chemputer?
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9 votes

I am curious to know if the word has been used in any way other than the above three ways. Mark. J. Winter at University of Sheffield has used the word differently — not as a term meaning something ...

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1 answers
10 votes
2k views
How to understand the crystal field splitting of d-orbitals in a trigonal prismatic geometry?
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9 votes

Is that related to crystal splitting? Yes. In case there are any doubts, the caption to the figure does make it clear that it's related to crystal field splitting, "(d) The splitting of d ...

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2 answers
5 votes
104 views
Is there a material where the conductivity drops when the current increases?
9 votes

This occurs in superconductors. In the simplest version (called type-I BCS superconductors) there is a resistanceless state at low temperature, magnetic field, and current density. When the current ...

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4 answers
13 votes
375 views
Is python sufficient for serious tensor network or DMRG calculations?
9 votes

I would argue that you can use a package like DMRG++, which is written in C++, without knowing much C/C++ or indeed any language. It has its own input format that takes some getting used to (...

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2 answers
8 votes
177 views
What will break the time-reversal symmetry?
8 votes

Another way to explicitly break time-reversal symmetry is by applying circularly polarized light. Under time reversal, left circularly polarized light transforms to right circularly polarized light, ...

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1 answers
10 votes
280 views
Does One-to-One Correspondence of Hohenberg Kohn Theorem Mean Bijective or Injective and How to Prove it?
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8 votes

I'm not familiar with the Carsten Ullrich text you mention. However, one possibility is that he followed Hohenberg and Kohn's example of assuming a non-degenerate ground state. If the ground state $\...

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2 answers
13 votes
326 views
Hubbard U correction for Copper
7 votes

I can't speak as to how the Materials Project selects what information to display, but it's clear that the Hubbard $U$ (or rather the correlations/interactions it attempts to capture) generally is ...

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3 answers
15 votes
1k views
Magnetism and Topology
7 votes

Topological magnon band structures Another way of combining topology and magnetism is to consider a magnetic insulator with non-trivial magnon band structure. This setting is somewhat different from ...

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1 answers
5 votes
63 views
Property related with Berry curvature: $\Omega_{n,\mu\nu}=-\Omega_{n,\nu\mu}$
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7 votes

You can just exchange the $\mu,\nu$ indices to verify the antisymmetry: $$ \Omega_{n,\mu\nu}(\mathbf{k})=\partial_{\mu}A_{n\nu}(\mathbf{k})-\partial_{\nu}A_{n\mu}(\mathbf{k})\\ \Rightarrow \Omega_{n,\...

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3 answers
24 votes
255 views
What are examples of materials that closely correspond to the Heisenberg model?
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7 votes

1D A famous example of a nearly ideal spin-$1/2$ isotropic Heisenberg antiferromagnetic chain (1D) system is copper pyrazine dinitrate [Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$], which was discussed in Hammar ...

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2 answers
5 votes
320 views
What is the meaning of these d states names?
6 votes

To add to Jack's answer, I'll point out that the $a$, $e$, $t$ etc. labels are symmetry labels of the orbitals in an irreducible representation (irrep). They are lower-case versions of their ...

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1 answers
7 votes
106 views
How is the error in a wavefunction related to the error in energy?
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6 votes

You can, in fact, do better as the answer to this Physics.SE question of yours indicates, assuming you're after an asymptotic expression. I haven't read the book you mention, but if you're familiar ...

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1 answers
2 votes
134 views
Has it been researched whether face centered cubic carbon is stable?
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6 votes

One of the papers citing the paper you linked is this paper : G. Murrieta, A. Tapia, and R. de Coss, Structural stability of carbon in the face-centered-cubic (Fm$\bar{3}$m) phase, Carbon 4, 771-774 (...

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1 answers
6 votes
80 views
Charge density wave and band inversion
6 votes

N. Mitsuishi et al. "Switching of band inversion and topological surface states by charge density wave," Nature Communications 11, 2466 (2020) may be of interest to you. I don't think there ...

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2 answers
7 votes
163 views
Why is there a large discrepancy between calculated frequency dependent dielectric function and experimental measurement?
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5 votes

It's not obvious to me that you are doing anything wrong in your calculation. Your result for the crossover energy seems consistent with the literature, e.g. Theodorou et al. (1999) and Petalas et al. ...

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1 answers
8 votes
116 views
Are there other kinds of stability of materials? How to demonstrate that with computation approaches?
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5 votes

Radiation stability In some applications or environments (e.g. fission/fusion reactors, space, sterilization of packaging), radiation effects are highly important and can cause significant damage to, ...

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