preparing a transversely polarized Ising configuration for relaxation

[dcyang]

Hi,
I have a question related to #1549 (TDVP) and #1672 (initial sample).
I've been trying to reproduce the results of Schmitt and Heyl (2018, 2020) with the transverse field Ising model.
One of their main results show the relaxation of a fully $x$-polarized spin configuration to a small transverse field.

My attempt at it was to use 2 Hamiltonians (nk.operator.IsingJax): first for equilibrating the system with a strong field (say $h = 99$) using nk.driver.VMC, and then pass the MCState to the second Hamiltonian with a weak field (say $h = 0.1$) using nkx.driver.TDVPSchmitt.

L = 4
ham1 = nk.operator.IsingJax(nk.hilbert.Spin(1/2, L*L), nk.graph.Square(L), h=99, J=-0.25)
# ... running VMC to equilibrate vstate1 ...
ham2 = nk.operator.IsingJax(nk.hilbert.Spin(1/2, L*L), nk.graph.Square(L), h=0.1, J=-0.25)
time_ev = nkx.driver.TDVPSchmitt(operator=ham2, variational_state=vstate1,
             integrator=nkx.dynamics.Euler(dt=0.01), holomorphic=True)

But it looks like the effect of the initial strong field remains in the MCState as we go to the relaxation stage, so there is an overall drift in the total spin in the $x$ direction (sum of nk.operator.spin.sigmax). Below are $S_x$ relaxation curves of a 4x4 system to $h = 2 h_c$ on nk.models.RBM which were first equilibrated with $8 h_c$, $16 h_c$, $32 h_c$ transverse fields. They show some oscillation but also drifts overall. So it seems to work partially ...

Q: Is there a way to "manually" prepare a fully $x$-polarized configuration, ie. without the field effects from the equilibration stage?
(or will I have to write a new nk.hilbert object?)

Thanks in advance.

[PhilipVinc]

Well, to prepare a fully polarised state I would set J=0.0.

To do it a bit more cleanly and efficiently, I would use the state learning fidelity minimisation example from netket_fidelity.
Just set J=0.0 in the example and you will be learning that state.

While this works starting from the state obtained through ED, it's trivial to write a 'variational ansatz' that prepares the fully polarised state (it's simply a constant function) that can be used for arbitrary sizes.

[PhilipVinc]

Furthermore, in my experience TDVP won't work with such large tilmestep.
You will need at most 1e-3 and possibly smaller.
If I remember correctly, Markus was using Heun in the PRL with adaptive time stepping (though adaptive time stepping is not very stable in my experience, so I'd suggest disabling it at the beginning).

Also, be sure to scan different values of rcond_smooth to find the one that works well.

[dcyang]

Took me a while to try all the things you said. The drift persisted even after setting $J=0$ to prepare a nk.VMC state or learning it with netket_fidelity, so I concluded that the initial config is only a partial cause of the issue.

I have since started experimenting with different nk.models and saw that the effect is much weaker for some models than others.
Thanks @PhilipVinc for pointing me in the right direction!