# Tag Info

## Hot answers tagged model-hamiltonians

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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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-...

### 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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### 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 ...
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### 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 ...
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### 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. ...
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### 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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### 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 ...
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