Hi, everyone. I'm working on calculating the infinite temperature correlation function \(\langle \hat{S}_i^z(t) \hat{S}_0^z\rangle_{\beta=0}\). The point is to evolve two states \(\lvert\psi\rangle\) and \(\hat{S}_0^z\lvert\psi\rangle\) and calculate the expectation value of \(\hat{S}_i^z\). The infinite temperature state \(\lvert\psi\rangle\) is generated by "PurificationMPS.from_infiniteT" without cooling. I know that "purification.PurificationTEBD" can be used to evolve an infinite temperature state. However, I'm dealing with a long range Hamiltonian. I guess I can only evolve the infinite temperature state by TDVP method. Yet it does not work (maybe TDVP is not suitable to evolve such a state?).

For simple \(J_1-J_2\) Heisenberg model, maybe I can group two sites and employ TEBD method? Is there a general method for general long range system? Does anyone have experience on this problem?

## How to evolve an infinite temperature state in a long range Hamiltonian system?

### Re: How to evolve an infinite temperature state in a long range Hamiltonian system?

At the moment, you should use tenpy.algorithms.purification.PurificationApplyMPO for models with long range.

(Or alternatively group sites and use the PurificationTEBD as you suggested.)

TDVP doesn't work with purification at the moment. Really, we should refactor the purification code a bit such that it works generically for arbitrary algorithms. I've opened an Issue #415 for this, although it will probably be quite a while until we can work on this. If someone is interested to implement this, pull requests are of course welcome

(Or alternatively group sites and use the PurificationTEBD as you suggested.)

TDVP doesn't work with purification at the moment. Really, we should refactor the purification code a bit such that it works generically for arbitrary algorithms. I've opened an Issue #415 for this, although it will probably be quite a while until we can work on this. If someone is interested to implement this, pull requests are of course welcome