32 votes
Accepted

Where is the extended Hückel method (EHM) still used today?

In an era of ab initio methods and many-body methods like the $GW$, there is not too much room for methods like the extended Hückel model to be the main method in any particular field of materials ...
19 votes
Accepted

When do we abandon ab initio methods?

There's three scenarios that come to my mind, for when ab initio methods get abandoned: The cost becomes prohibitive (e.g. too many electrons) The insight is lost It is simply not required for what ...
  • 29.1k
18 votes

Where is the extended Hückel method (EHM) still used today?

One area where the extended-Huckel method continues to see use is to form the initial guess for an SCF calculation or even just a more accurate semi-empirical method. While most electronic structures ...
  • 14.3k
17 votes
Accepted

Ising model: How can I spot the critical point?

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 ...
  • 4,238
16 votes
Accepted

Why is uncertainty not a big problem in computational chemistry?

Following your arguments, we would see also a 'violation' of the Heisenberg uncertainty principle (HUP) in single-particle quantum mechanics, e.g. in a Hamiltonian of a particle in an external ...
  • 473
14 votes

Ising model: How can I spot the critical point?

As Anyon correctly pointed out, there is no phase transition at finite temperature in 1D. In 2D there are a number of different ways to identify the phase transition (I'm assuming you're using Monte ...
14 votes

Where is the extended Hückel method (EHM) still used today?

I know of at least one place, where it is relatively common to use the extended Hückel theory in practise: in generating initial guess orbitals for further electronic structure calculations. The most ...
12 votes
Accepted

Is Heisenberg model or in its simplier form Ising model a good approximation to study magnetic systems?

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 ...
  • 4,238
12 votes

Why is uncertainty not a big problem in computational chemistry?

Indeed, due to the uncertainty relation, the electrons in a molecule do not have a definite potential energy, nor do they have a definite kinetic energy (yet they have well-defined expectation values ...
  • 7,463
11 votes

Is there a list of models that do and do not have the QMC sign problem?

You can tell if a Hamiltonian is sign-free by looking at it in the form that it is handed to you. If the Hamiltonian is real and the off-diagonals are non-positive then it is Stoquastic (which is sign-...
11 votes

Is there a list of models that do and do not have the QMC sign problem?

The general problem of determining whether a Hamiltonian can be transformed into "stoquastic" (i.e. sign-problem-free) form by local transformations is NP-hard: https://arxiv.org/abs/1906.08800 ...
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11 votes
Accepted

Is there a list of all universality classes for phase transitions with examples of each?

A locally interacting system displaying a continuous phase transition belongs to a universality class that is determined solely by the system symmetries and dimensionality. Drawing from Wikipedia's ...
  • 786
10 votes
Accepted

Autocorrelation function problem in Monte Carlo simulation of 2D Ising model

First, some general remarks: The measurements should be made after the system has equilibrated, i.e., a large number of the first iterations should be discarded before the analysis. They should also ...
  • 786
10 votes
Accepted

How to use wavefunctions/density to determine which orbitals lead to edge states?

One way of determining this is using the projected density of states (P-DOS) This resolves the DOS into specific orbitals thereby allowing you to discretize each orbitals weight for a specific energy. ...
  • 1,814
9 votes
Accepted

How to construct a Tight-Binding Hamiltonian from first-principles computations?

Yes! It is definitely possible and it is useful for calculating other things like electronic transport and first-principles values of Hubbard U (i.e. the ACBN0 method, which I have used a bit). Some ...
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9 votes
Accepted

What class of materials are closest to realizing the tunable coupling Hamiltonian?

Realizing this Hamiltonian in a natural material I cannot imagine a material in which all nearest-neighbor spin-spin interactions can be adjusted arbitrarily at the same time. Spin-spin couplings ...
  • 29.1k
9 votes
Accepted

Proper handling of change of units in numerical calculations

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 \...
  • 4,238
9 votes

Why is uncertainty not a big problem in computational chemistry?

A common textbook statement of the uncertainty principle is: $$\tag{1} \Delta x \Delta p \ge \frac{\hbar}{2}, $$ where $\Delta x$ and $\Delta p$ are the uncertainties in measurements of the position $...
  • 29.1k
8 votes
Accepted

What are examples of materials that closely correspond to the Heisenberg model?

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 ...
  • 4,238
8 votes

Autocorrelation function problem in Monte Carlo simulation of 2D Ising model

@stafusa's answer is great, but there is a specific phenomenon you are encountering here called critical slowing down, which is especially bad for the single-spin-flip Metropolis Algorithm. Near the ...
8 votes

Ising model: How can I spot the critical point?

I think Anyon's and taciteloquence's answers are perfect. I just want to add an emphasis on the following fact that frequently leads to confusion for beginners. The formal definition of the ...
8 votes

Help with translating Hamiltonian into matrix

For this type of calculation, I find MATLAB/Octave to be easier, at least for demonstrating what to do. You can add the np. everywhere afterwards if you want to use ...
  • 29.1k
7 votes

How to derive the effective Hamiltonian of two-dimensional TMDCs monolayers?

How do you get the Hamiltonian formula for transition metal dichalcogenides? How to derivate the expression above (equation (1))? You can use the $ k \cdot p$ method to derive this effective ...
  • 14k
6 votes

How to calculate the potential in Hubbard-U correction and when to apply it?

I assume you mean including a Hubbard U potential within a Kohn-Sham density functional theory (DFT) calculation. The main reason why you might wish to do this is because you are studying a material ...
  • 4,382
6 votes

What measured quantity can be associated to the value of the J parameter in the Heisenberg/Ising hamiltonians?

Here I'll assume that the material is already believed to be roughly described by a model of the Heisenberg or Ising form. In that case, you just want a quantity that is easy to measure in your ...
5 votes

Ising models with many-body interactions

As a (very) incomplete answer to this question, here is one paper discussing the Ising FM with a plaquette term. Here specifically chosen because there was not a good cluster algorithm for it (so they ...
5 votes

Is there a list of all universality classes for phase transitions with examples of each?

I felt that it's important to note that not all universality classes are determined solely by spacial dimension and symmetry, even when the interactions are local. The easiest model that exemplifies ...
5 votes
Accepted

What are the physical consequences of adding a constant to the diagonal of the effective Hamiltonian of monolayer materials?

I will assume that we are working with a Hamiltonian in some tight-binding-like position basis (where each row/column in $H$ is a localized orbital). Essentially the constant you are adding acts as a ...
5 votes

Are there interesting applications of estimating the energy for generalizations of the Heisenberg model?

When you have more than two Pauli operators in a single term, you can model multipolar terms, as described in this paper: ... multipolar correlators of order $p=1$ (spin, dipolar), $p=2$ (quadrupolar)...
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4 votes

How can I calculate the J value in an antiferromagnetic material?

In the attached paper they have used the broken symmetry method to calculate the exchange. Assuming that you're dealing with a 1D chain of spins. you can do this using quantum ESPRESSO via the ...
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