Hi,
I am trying to do a problem where the Hamiltonian has some variant of terms like the onsite transverse field term (Sx) in the TFIM.
I want to use quantum number conservation for efficiency but I am running into problems due to the presence of the onsite Sx term which does not conserve the flux in the Hamiltonian.
Is there any way around it.
If it were Heisenberg I could have written S_x S_x + S_y S_y term as 1/2 S_+ S_- + S_- S_+ but in my case the term is onsite. How do I make sure that the flux is conserved?
If you could tell me the solution from the point of view of TFIM, I think I could extend the logic to my problem as well.
If the system does not possess a certain symmetry, then you cannot use it (because it does not exist), and there is no way around that.
Sometimes there is a subgroup of a symmetry under which the Hamiltonian remains symmetric. In the case of the transverse-field Ising model there is a “Z2 parity” symmetry (flipping all the spins) that can be used even though the U(1) total Sz conservation is not a symmetry. But the parity symmetry is not a particularly useful one for speeding up calculations since it only leads to two blocks per tensor (i.e. not very sparse). But sometimes there are “physics” reasons to want to conserve symmetries like that, such as for investigating phase transitions or comparing to experiments on closed systems.
Okay even if there is not much numerical advantage, still could you please tell me how to use just the parity symmetry in my quantum number definition?
To conserve only Z2 parity, pass only the keyword argument conserve_szparity=true to the siteinds function when making your site indices. This keyword argument is recognized for the "S=1/2" site type.
I would encourage you to print out your site indices to double check and confirm that only parity quantum numbers are being conserved.