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24

2003: Book chapter by Karen Hallberg. 2004: Reviews of Modern Physics by Ulrich Schollwoeck (2818 current citations). 2006: Advances in Physics by Karen Hallberg. 2008: JCTN: by Gabriele De Chiara and co-workers. 2011: ARPC: by Garnet Chan and Sandeep Sharma (426 current citations). 2014: The European Physical Journal D by Sebastian Wouters and Dimitri Van ...


11

There probably are good Python bindings to various DMRG implementations, which allow one to run DMRG from Python. Since the implementations typically rely on lower-level C/C++/Fortran routines, the calculations run quite quickly. E.g. PySCF appears to have bindings to various DMRG programs, see https://sunqm.github.io/pyscf/dmrgscf.html. If you're talking ...


9

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 (unfortunately it isn't overly well documented), but the outputs are provided in text and hdf5 formats that you can then manipulate with your favorite scripting language -...


8

I've heard people talking about working on tensor networks for electronic structure since the 2000s, but here in the 2020s I'm aware of no code that can help me solve the problems in which I'm interested. I think "serious" tensor network codes for electronic structure are still a "dream", and I'm becoming more and more doubtful that any ...


7

For 1D spin Hamiltons it is perfectly doable even if you code from scratch. NumPy should be sufficient. I have written DMRG codes in both Julia and python and I see no difference, this is also due to the fact that I am a newbie in Julia and my codes are far from good. However, if you are willing to use python I will suggest you to do all the algorithm level ...


5

There's two later review articles by Schollwöck that weren't in Nike's excellent list: 2011: Phil. Trans. R. Soc. A (2011) 369, 2643–2661 2011: Annals of Physics 326 (2011) 96–192


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p-DMRG Perturbatively corrected DMRG by Sheng Guo, Zhendong Li, and Garnet Chan (in 2018). Motivation: DMRG scales poorly with respect to the number of basis functions. the above paper says that DMRG's cost is $\mathcal{O}\left(M^3D^3\right)$ for $M$ basis functions and a bond dimension of $D$, and that $D$ often has to scale as $\mathcal{O}\left(M\right)$, ...


4

The iDMRG algorithm is tailored for translationally invariant 1D systems with area law ground states (gapped states). If that's what you're interested in, iDMRG is hard to beat for accuracy, assuming it does converge to the ground state. (In some cases, analytical solutions by e.g. the Bethe ansatz are possible. They may offer an improvement, but it can be ...


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