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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 that we name it after him. However I completely disagree with the sentence that you have quoted. Keep in mind that even though the Nobel Lecture was in 1999, Kohn ...


17

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 VASP, Quantum Espresso and Medea-VASP. It is undergraduate level introduction to the subject Materials Modelling Using Density Functional Theory: Properties and ...


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"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 the exponential wall encountered in full configurational interaction methods?. The cost of FCIQMC still scales exponentially with respect to the number of ...


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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 Hamiltonian $\hat{H}$, the $\tau$-dependence can be solved in a way analogous to the usual time dependence to obtain: $ \psi(x,\tau)=\sum_nc_n(0)e^{-E_n\tau/\hbar}\...


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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-free). Moreover, every Hamiltonian is sign-free if you don't care about the computational complexity of transforming it: In the basis that it is diagonal, the ...


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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 https://arxiv.org/abs/1802.03408 On the other hand, there are lots of individual Hamiltonians for which people have figured out clever tricks to bring them into ...


10

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 largest size that is practical with your computational resources. Case in point: people do finite size scaling with extremely small sizes for exact ...


10

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 be averaged over a number of runs, in order to reduce noise. This plot is better appreciated with a log scale in the vertical axis. Later on, it's important to ...


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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 DMC will not converge to the fermionic ground state of interest in electronic systems. To force the system to project out the fermionic ground state, then the ...


9

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 always, is in the details. Since we can solve Schrodinger and Dirac equations arbitrary accuracy (see eg Nakatsuji's work, http://qcri.or.jp/~nakatsuji/nakatsuji....


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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-size gap $\Delta \propto 1/L$, so to stay consistently above or below that finite-size gap, $\beta$ is typically set to scale as $\beta = cL$, where $c$ is some ...


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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 material as complicated as gold, but I'm not an expert in this field by any means. This article discusses structural optimization with VQMC: S. Tanaka J. Chem. ...


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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 more accurate than DFT, so it is often taken as a reference for solid state calculations. Indeed, the pioneering QMC calculations of the electron gas by ...


8

@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 critical point, the typical cluster size diverges. For the single-spin-flip algorithm, it's really hard to flip these huge clusters, so the autocorrelation ...


7

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 Hamiltonians in any number of dimensions. The method works by expanding the partition function in a Taylor series $$\tag{1} Z = \mathrm{Tr}[ \rho] = \mathrm{Tr}[e^{-\...


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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 comprising $M$ basis states; this has a computational cost $O(MN^2)+O(N^3)$ diagonalise a dense Hamiltonian matrix in the subspace of $N$ trial states, which has ...


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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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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 not always be obvious why. There is probably not one method that will work best generically. For quantum spin systems in $d\geq 2$ (lattice Hamiltonians with ...


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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 advanced) introductions to these topics can be found in Thijssen's Computational Physics. What's nice about it is that it covers the theory, provides coding (as ...


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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 to have a parallelization efficiency of 99.7% up to at least 24800 cores. It does FCIQMC and has been used on Hubbard models in several papers, perhaps the most ...


2

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 on its website) and has been cited in dozens of publications since its release in 2017. The package is very flexible, as it can simulate any Hamiltonian that ...


1

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 can all be restarted when the calculation has to stop for whatever reason. Since you pointed out that ACFDT-RPA calculations cannot be restarted, the ability to ...


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