Queries Related to Quantum Number Wrapper, Basis State Construction for Custom Hamiltonian

[JessicaJohnBritto]

Hamiltonian: 1D Bose Hubbard Model. Fixed number of particles, no spin degrees of freedom.
Basis States are in the occupation number basis. For eg, in case N = 2 sites, k = 2 bosonic particles in the entire system, the basis states are (2, 0), (1, 1), (0, 2) --- where (x1, x2) - means x1 no. of particles on site-1 and x2 no. of particles on site-2, and their sum should be equal to k, i.e, sum(occupation number basis) = k --- k-constraint.
n_max - max no of particles each site can hold.

I have been trying to follow the example given in Custom Hamiltonian section to use it for my model.

1. Could you please tell me what this 1 after the Q-tuple means in this (Q(0, 0, 0), 1)?
2. Can I generate all the possible states in a list and pass it to Q?
3. What does SX do in Q = driver.bw.SX? I understand bw - is the object of Block2Wrapper.
4. In the driver.initialize_system - how can I impose k-constraint on Q(n_max, n_max)?
5. In this code - b.add_term("cd", np.array([i for i in range(L) for _ in range(4)]), U), is 4 being used since for each site for the hopping term, when it is flattened, we get 4 elements, so to keep the length of the vector same for Hopping and onsite interaction terms - site_index is being repeated 4 times for each site?

I am getting AssertionError in each of the following lines

• basis = [(Q(2, 0), 1), (Q(1, 1), 1), (Q(2, 0), 1)] # [0ab2]
• driver.initialize_system(n_sites=L, vacuum=Q(0, 0), target=Q(n_max, n_max), hamil_init=False)

Here's the link to the notebook for this case.

Thanks

[hczhai]

I have added an example script for the Bose-Hubbard model in the updated documentation.

Could you please tell me what this 1 after the Q-tuple means in this (Q(0, 0, 0), 1)?

The 1 is number of states per quantum number, which is explained in the documentation: "The quantum number and number of states in each quantum number at each site (which defines the local Hilbert space) is set in site_basis."

I am getting AssertionError in each of the following lines

To solve these problems, please read the documentation carefully. For example, the documentation says: "The number of arguments in the quantum number wrapper Q should then match the number of sub-group names given in DMRGDriver.set_symmetry_groups."

In this code - b.add_term("cd", np.array([i for i in range(L) for _ in range(4)]), U), is 4 being used since for each site for the hopping term

This line of code is not part of the documentation.

[JessicaJohnBritto]

Yes, it's cleared now. Thank you!