### Implementing non on-site symmetries

Posted:

**15 Oct 2020, 14:14**Hello,

I am planning some large scale iDMRG simulations of a 2D spin model on the cylinder. The model has a global U(1) symmetry which could be exploited, corresponding to on-site particle number conservation in an analogous fermionic formulation of the model. In the spin language, however, the number operator maps into a star operator (up to constants):

\(N=\sum_i n_i=\sum_{i}\frac{1-\sigma^x_{i,i+\hat{x}}\sigma^x_{i,i-\hat{x}}\sigma^x_{i,i+\hat{y}}\sigma^x_{i,i-\hat{y}}}{2}\)

and therefore it is not on-site. I was wandering if implementing such multi-site conserved charges is something that can be done, and how much effort it would require given the current status of TeNPy. Of course I would be happy to contribute to the task, but at the moment I do not have enough knowledge of how np_conserved works to even tell if this is feasible, so I would like to hear the opinion of someone more expert then me on the matter.

Thanks!

I am planning some large scale iDMRG simulations of a 2D spin model on the cylinder. The model has a global U(1) symmetry which could be exploited, corresponding to on-site particle number conservation in an analogous fermionic formulation of the model. In the spin language, however, the number operator maps into a star operator (up to constants):

\(N=\sum_i n_i=\sum_{i}\frac{1-\sigma^x_{i,i+\hat{x}}\sigma^x_{i,i-\hat{x}}\sigma^x_{i,i+\hat{y}}\sigma^x_{i,i-\hat{y}}}{2}\)

and therefore it is not on-site. I was wandering if implementing such multi-site conserved charges is something that can be done, and how much effort it would require given the current status of TeNPy. Of course I would be happy to contribute to the task, but at the moment I do not have enough knowledge of how np_conserved works to even tell if this is feasible, so I would like to hear the opinion of someone more expert then me on the matter.

Thanks!