Monday, March 16, 2015

Relative merits of different numerical methods for correlated fermions in 2D

This helpful table appears in a review article
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group 
E.M. Stoudenmire and Steven R. White

The review also shows that comparisons of the 2D DMRG with methods such as PEPS and MERA (heavily promoted by quantum information theorists) imply that 2D DMRG performs significantly better.

I thank Seyed Saadatmand for bringing the table to my attention.


  1. From the last section of the review, it seems that the tensor network methods are related to DMRG, and that there are cases in which iPEPs is better than 2D DMRG.

    "At some width, which depends on how large an m or D can be treated with current computing resources, DMRG becomes less accurate than iPEPS."

    Whether one should use DMRG or iPEPS depends primarily on whether the bulk behavior can be extrapolated with cylinders smaller than this width. Alternatively, it can be very useful to use both DMRG and iPEPS or MERA, and compare results.

    1. Andrew,

      Thanks for the comment.
      I agree it is very useful to compare the alternative methods.

      My only comment is that iPEPS and MERA have not lived up to some of the hype I have heard about them.

  2. Unfortunately the paper is behind a paywall. Nonetheless I'm intrigued that apparently people seem to have implemented world-line techniques in 2 dimensions. My impression was that world-line QMC worked very well in 1D, and although in principle it could be used in higher dimensions, it was too fiddly for anyone actually to use it. Has some advance been made?

  3. The paper is freely available at