Timeline for Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?
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| Dec 4, 2015 at 2:11 | comment | added | mr.no | @MengCheng I have talked with professor Tao Xiang. He thinks that this algorithm by F.Verstraete(arXiv:cond-mat/0404706) and White(arXiv:0801.1947) is not widely emplyed because of its low efficency even improved by White. Maybe also it's not stable when solving the generized eigenvalue problem(Hx = lamda Nx). But even for its low efficency, F.Verstraete found the reason why traditional DMRG have poor result in PBC(Its wave function should be approximated by mps in PBC, while in traditonal DMRG it has been assumed to be mps in OBC even the pysical system is in PBC). | |
| Dec 3, 2015 at 16:40 | comment | added | Meng Cheng | The algorithm in arXiv:0801.1947 invoked a crucial approximation at Eq. 8, which truncated the product of transfer matrices. My impression (by talking to DMRG/MPS experts) is that this way of truncation is rarely employed in practice even nowadays. Maybe @NobertSchuch can comment more on the algorithm. | |
| Dec 3, 2015 at 16:13 | comment | added | Norbert Schuch | @MengCheng I certainly agree. | |
| Dec 3, 2015 at 16:07 | comment | added | Meng Cheng | @NorbertSchuch I agree, finitely correlated states were written down roughly around the same time as the original DMRG. But maybe it is fair to say that the importance of MPS in 1D was fully appreciated after the relation to DMRG was uncovered. | |
| Dec 3, 2015 at 9:01 | comment | added | mr.no | @NorbertSchuch I agree with you. MPS has been discovered before DMRG. But its power in simulating 1D quantum systems was found in DMRG. | |
| Dec 3, 2015 at 8:57 | history | edited | mr.no | CC BY-SA 3.0 |
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| Dec 3, 2015 at 8:49 | comment | added | mr.no | @MengCheng "But even with MPS the PBC is hard to deal with"--How about the VMPS by F.Verstraete(arXiv:cond-mat/0404706) and then improved by White(arXiv:0801.1947)? In these two papers they said that mps in PBC can get much better results than traditional DMRG even as good as traditional DMRG in OBC. | |
| Dec 2, 2015 at 8:04 | comment | added | Norbert Schuch | "Historically MPS was discovered by inspecting the wavefunction obtained in DMRG" -- I (partly) disagree. MPS-like ansatzes were known before, such as the Finitely Correlated States of Fannes-Nachtergaele-Werner (but I'm pretty sure such ansatzes had been written down before). | |
| Dec 2, 2015 at 6:00 | comment | added | Meng Cheng | Historically MPS was discovered by inspecting the wavefunction obtained in DMRG, and when the full power of MPS was unravelled DMRG is reformulated with MPS. But even with MPS the PBC is hard to deal with -- although there is a very powerful method for infinite system, usually called iDMRG. | |
| Dec 2, 2015 at 4:55 | history | answered | mr.no | CC BY-SA 3.0 |