Hi,

I am using iDMRG to calculate the entanglement spectrum of my model. Our model consists of three site unit cells with two sites being spin-half fermionic and one bosonic. My aim is to find the degeneracies in the entanglement spectrum to confirm our analytical calculation of the existence of an SPT in certain parameter regimes of our model.

I am confused about what to choose as the error bar in the calculated entanglement spectrum. I have come up with a handwaving error estimate based on the norm error. Since in the paper https://arxiv.org/abs/0910.1811, the canonical condition involved the \Lambda matrices. I claim that the error in the entries of \Lambda matrix is given by the square root of the norm error.

Is there a better or an inbuilt way to extract the error in the entanglement spectrum? Depending on the chosen error bars, I either observe a degeneracy or not for some of the values in the entanglement specturm. I would appreciate any input from the community.

Cheers

Dhruv

## Error bar in the calculated entanglement spectrum

### Re: Error bar in the calculated entanglement spectrum

Whit error bar you mean "what values do I consider degenerate"?

Don't choose that value too small based on what the norm error is: the error in the entanglement spectrum depends drastically on how high the value is. If you plot the full spectrum up to the chi_max, the highest values in the entanglement spectrum correspond to the schmidt values you almost discarded - and those are naturally affected most by the trunctation. You should only trust the lower parts of the entanglement spectrum to a high accuracy. From a practical point of view, choose the value sensible given the discrete spacing between schmidt values in the lower part of the spectrum - you only need to distinguish between "all" or "just a few" degeneracies for the classification.

Don't choose that value too small based on what the norm error is: the error in the entanglement spectrum depends drastically on how high the value is. If you plot the full spectrum up to the chi_max, the highest values in the entanglement spectrum correspond to the schmidt values you almost discarded - and those are naturally affected most by the trunctation. You should only trust the lower parts of the entanglement spectrum to a high accuracy. From a practical point of view, choose the value sensible given the discrete spacing between schmidt values in the lower part of the spectrum - you only need to distinguish between "all" or "just a few" degeneracies for the classification.

### Re: Error bar in the calculated entanglement spectrum

Thanks a lot for your reply.

I took into account the lower part of the entanglement spectrum and obtained convincing results

I took into account the lower part of the entanglement spectrum and obtained convincing results