On Apr 21, 2011, at 3:07 PM, 孙照宇 wrote:
Thank you very much for the reply ! Now I have another question about DMRG of finite version.
By using infinite DMRG method, first I increase the size of the system to 2L. Then I use the finite DMRG method with 2L fixed. After finite-size sweeping for 6-10 times, the energy of the system converges very well. However, when paying attention to the correlation function, I am confused by the following results.
In the infinite-method procedure, I have obtained the size-dependence of the correlation function of the two sites in the middle of the chain. which we label as G(i), i=1,2,...,2L. While in the finite procedure, after several sweep, I also obtain a position-dependence of the same two-site correlation function, which we label as P(i), i=1,2,..., 2L. P(i) is converged and the curve (or shape) does not change any more with further finite-size sweeps, just like the energy.
Sometimes I find the shape of G(i) is very similar to the converged shape of P(i), which means that the ground-state wave-function can be obtained accurately by the infinite method and the finite-size sweep is not needed at all. Please see "good.png".
However, sometimes the shape of G(i) is quite different from the shape of P(i), which seems that the ground-state wave-function obtained with the infinite-method is quite inaccurate. Please see "bad.png".
Now my question is: The infinite-method result is the starting point of the finite-size sweep. Suppose the starting point (the results from the infinite-method ) is not reliable. Then the following finite-size sweep is still credible or not incredible at all ? I'd like to mention that the energy of the system converges very well in the finite-size sweep.
Any comments are valuable to me.
The case that the infinite size method gives you a "bad" result is rather common and the sweeps typically improve it and converge to the true ground state. However, you can always be trapped and a careful analysis of the data is always needed.
Matthias