How can I extrapolate a nonlinear curve to D->Inf limit?
Hi everyone, I'm reading DMRG tutorials in http://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:DMRG-01_DMRG. and http://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:DMRG-02_Gaps It suggested me to extrapolate energies and energy gaps to D(maxstates) -> infinity. The question is about nonlinear extrapolation. In the case spin 1/2 gap versus 1/L, there is a linear relation and I can easily polyfit it linearly and get the gap in L->Inf limit. But in the case of quantities such as gaps versus D(maxstates), there is no simple linear relation. For example: Each time I enlarge D by 50, energy gaps change by the following values: [ -2.49851713e-08, -1.45270462e-11, -2.84217094e-14, -5.50670620e-14] which slows down changing by smaller and smaller values. I have done some exponential curve fittings in matlab but it become confusing when you have many models to fit it. How can I extrapolate such a nonlinear curve to D->Inf limit? Is there any standard way to do this? LiuBiao ll070616@126.com
To calculate gaps accurately for finite systems, you really should be in the limit where the energies are converged with respect to the bond dimension, so that you only have to do a scaling with respect to the system size. If your energies are not converged with respect to D, then you should extrapolate separately the groundstate and excited state energies to large D (for finite systems, this is normally done with a 2nd degree polynomial fit; for infinite systems it is linear). You should be careful to get a reliable estimate of the error of the fitted energies, since you may find that the error bars are larger than the gap that you want to find. Regards, Ian ----------------------------------------------------------------------- Dr Ian McCulloch ianmcc@physics.uq.edu.au ARC Future Fellow School of Mathematics and Physics The University of Queensland smp.uq.edu.au/profile/168/ian-mcculloch Tel: +61-(0)450-461-283 WeChat ID: ianmcculloch1 ----------------------------------------------------------------------- On Thu, 27 Sep 2018, adfws wrote:
Hi everyone,
I'm reading DMRG tutorials in http://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:DMRG-01_DMRG. and http://alps.comp-phys.org/mediawiki/index.php/ALPS_2_Tutorials:DMRG-02_Gaps It suggested me to extrapolate energies and energy gaps to D(maxstates) -> infinity.
The question is about nonlinear extrapolation. In the case spin 1/2 gap versus 1/L, there is a linear relation and I can easily polyfit it linearly and get the gap in L->Inf limit. But in the case of quantities such as gaps versus D(maxstates), there is no simple linear relation. For example: Each time I enlarge D by 50, energy gaps change by the following values: [ -2.49851713e-08, -1.45270462e-11, -2.84217094e-14, -5.50670620e-14] which slows down changing by smaller and smaller values. I have done some exponential curve fittings in matlab but it become confusing when you have many models to fit it. How can I extrapolate such a nonlinear curve to D->Inf limit? Is there any standard way to do this?
LiuBiao ll070616@126.com
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participants (2)
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adfws
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Ian McCulloch