H = -\sum_{i}\sigma_{i}^{z}\sigma_{i+1}^{z}\sigma_{i+2}^{z} - h\sum_{i}\sigma_{x}^{i}
I am using the code given in DMRG Examples · ITensors.jl to compute the first excited state.
Now , while running my code I see that changing the value of noise affects the first excited state’s energy. From changing the noise to 10^{-8} to 10^{-6} I get much much better result. I say ‘better’ because I was doing some small L and crosschecked with ED. So my question is:
What is the wisest procedure to fix the value of noise ? On what things it may depend particularly when I am accessing systems size of the order of 100 or 200.
Hi Sourav,
While it’s a good question about how best to choose the value of the noise, I would say unfortunately there isn’t such a clear theory known for it. So you will need to just use intuition and some experience on smaller system sizes or easier limits of the system you are studying to find the answer for your case. (It’s really good you are cross checking with ED.) My intuition here is that too small of a noise value might be effectively the same as having no noise at all, so raising it helped to get the benefits.
I would say a rough argument for how to set it might be to make it as large as you can while seeing that it helps the energy to go down (versus choosing smaller noise). Then if raising it even larger makes the energy start to go up (versus smaller noise values) or make the energy start to oscillate or fluctuate as a function of DMRG sweeps, then it’s become too large.
These days, there are some more sophisticated descendents of the noise term idea that have been developed and we are in the process of researching them for future versions of ITensor. Some of these are able to automatically select the noise strength, based on gradient descent ideas. But they aren’t quite available in ITensor yet. Your question is helpful motivation for us to keep working on these though.
