37
votes
Accepted
Was Walter Kohn wrong about this?
Kohn is easily one of my favorite humans of all time, and he was a role model to whom I looked up in great admiration for most of my academic life; in fact before this site was created, I proposed ...
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17
votes
What are good resources to learn Materials Modeling?
I would recommend to start with Computational Materials Science: An Introduction by June Gunn Lee, The book starts from the basics and covers Molecular Dynamics and DFT featuring DFT exercises using ...
- 8,802
16
votes
How to explain to a five year old why "DFT with local exchange–correlation functionals do(es) not describe van der Waals interactions accurately"?
Standard DFT functionals are based exclusively on local information, e.g. for a GGA functional
$$ E_{xc} = \int n({\bf r}) \epsilon_{xc}(n({\bf r}), \nabla n({\bf r})) {\rm d}^3r $$
while van der ...
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12
votes
Accepted
Deep Neural Networks: Are they able to provide insights for the many-electron problem or DFT?
"However, it is notorious due to the exponential wall"
That is completely true, though there's indeed some methods such as FCIQMC, SHCI, and DMRG that try to mitigate this:
How to overcome ...
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11
votes
What are the types of Quantum Monte Carlo?
DMC (Diffusion Monte Carlo)
Theory. Consider the Schrödinger equation in imaginary time $\tau=it$:
$$
-\hbar\frac{\partial\psi(x,\tau)}{\partial\tau}=\hat{H}\psi(x,\tau).
$$
For a time-independent ...
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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-...
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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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10
votes
How to explain to a five year old why "DFT with local exchange–correlation functionals do(es) not describe van der Waals interactions accurately"?
I'll turn my comment as an answer, as requested by the OP and Nike.
Susi Lehtola's answer has already pointed out that dispersion (which may be a more accurate term than van der Waals interaction here)...
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10
votes
Accepted
How can very small lattices be sufficient for Quantum Monte Carlo simulations?
I think you are correct that there is an aspect of "take what you can get" to the sizes that are typically used in numerical methods. Even with finite size scaling (FSS), you usually try to go to the ...
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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 ...
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10
votes
What are the types of Quantum Monte Carlo?
FN-DMC (Fixed-node diffusion Monte Carlo)
Theory. See my answer about DMC. The only addition for FN-DMC is that the ground state of an arbitrary Hamiltonian will not be antisymmetrized, and therefore ...
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9
votes
How accurately are magnetic effects treated in *ab initio* methods?
It is an example where representative of different fields would give you very different answers. I do not want to pretend my answer would be by anyway complete.
Short answer: yes. And the devil, as ...
- 1,797
9
votes
Order of scaling for different algorithms
From my experience with Stochastic Series Expansion (SSE) QMC (a type of discrete-time QMC) the computational cost scales like $\beta L^d$.
In practice, it's often important to account for the finite-...
- 6,569
9
votes
Accepted
QMC calculation of the equation of state of metals
Given that variational quantum Monte Carlo (VQMC) is specifically for calculating ground state properties, it shouldn't have any problem with finding the $T=0$ energy.
It may be difficult to do a ...
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8
votes
Are QMC calculations practical for periodic structure calculations?
Quantum Monte Carlo (QMC) calculations in various forms, for example variational QMC or diffusion QMC have been used to study periodic systems for decades. In most cases, they provide results that are ...
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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 ...
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7
votes
Accepted
What are the types of Quantum Monte Carlo?
Stochastic Series Expansion (SSE) Monte Carlo
Theory: SSE is a finite-temperature, discrete-time technique that works well for quantum spin problems (e.g. Heisenberg model) and other lattice ...
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7
votes
Order of scaling for different algorithms
Conventional implementations of Kohn-Sham DFT scale cubically with system size. This is principally because at some point they:
orthonormalise a set of $N$ trial states, each expressed in a basis ...
- 6,467
6
votes
Is there a "gold standard" method in materials modeling for obtaining ground state energy?
I think the answer is probably: yes, but not just one. Or no, if you want to be very strict.
Depending on the type of system you are studying, different methods may work better or worse and it may ...
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5
votes
Accepted
Support for orbital-space Quantum Monte Carlo in CASINO?
CASINO is a continuum quantum Monte Carlo code, allowing you to perform variational and diffusion quantum Monte Carlo.
Best wishes,
Neil.
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4
votes
What are good resources to learn Materials Modeling?
This question is a bit old now, but hopefully my answer can complement Thomas's for anyone who comes across it.
While "materials" is not in the name of the book, I think great (though more ...
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3
votes
What packages exist for building quantum Monte Carlo simulations of spin or Hubbard Hamiltonians?
NECI (N-electron configuration interaction solver)
This is a free and open-source software written mainly in FORTRAN but with components in C/C++ and Python. It has been shown on a FeMoco calculation ...
- 33.1k
2
votes
What packages exist for building quantum Monte Carlo simulations of spin or Hubbard Hamiltonians?
ALF (Algorithms for Lattice Fermions)
This is an auxiliary-field quantum Monte Carlo package. It's free, open-source, actively maintained (current version: 2.0, with 2.1 on the works — news are posted ...
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1
vote
What are the advantages/disadvantages of QMC over ACFDT-RPA?
Advantage for QMC:
While this question is quite open ended due to there being at least 15 different types of QMC, one thing that all 15 of those methods have in common is that as far as I know they ...
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