BUG in periodic TEBD

[TanTsiChen]

Dear Johnnie I'm trying to do a quench, like for a up state with periodic boundary condition (PBC), and use the Hamiltonian qtn.NNI_ham_ising(L=10, j=4, bx=1, cyclic=True) to do the time-evolution. The result shows that the NNI doesn't have a periodic boundary condition, if you check the energy of in & out state (by using the Hamiltonian qtn.MPO_ham_ising(L=10, j=4, bx=1, cyclic=True)), the energy is not conversed, and if you use the Hamiltonian without PBC (qtn.MPO_ham_ising(L=10, j=4, bx=1)), you will see that the energy conversed though the time-evolution. Qicheng Tang

[jcmgray]

Yes I had forgot to test the cyclic case and hadn't added the final, extra odd gate between sites (n-1, 0). It seems to be working fine now - I'll add your example as a unit test case.

Note that the compression will not be optimal in the PBC case - might be worth having a play around with split_opts.

[TanTsiChen]

Yes I had forgot to test the cyclic case and hadn't added the final, extra odd gate between sites (n-1, 0). It seems to be working fine now - I'll add your example as a unit test case.

Note that the compression will not be optimal in the PBC case - might be worth having a play around with split_opts.

Oh, i had tried to add the final gate, but i forget that in python the counting is from 0 to n-1, not 1 to n (i'm just starting using python :-D)

[jcmgray]

Oh, i had tried to add the final gate, but i forget that in python the counting is from 0 to n-1, not 1 to n (i'm just starting using python :-D)

Don't worry it soon becomes second nature!

I've pushed a fix here. Let me know if this resolves the issue for you and then I will close this.

[TanTsiChen]

Oh, i had tried to add the final gate, but i forget that in python the counting is from 0 to n-1, not 1 to n (i'm just starting using python :-D)

Don't worry it soon becomes second nature!

I've pushed a fix here. Let me know if this resolves the issue for you and then I will close this.

Okay, it well works now.

[jcmgray]

Just to elaborate on the bit about compression (in response to email):

The difference is that in the OBC you can always put the MPS in canonical form.

In [1]: import quimb.tensor as qtn

In [2]: psi = qtn.MPS_rand_state(20, 10)

In [3]: psi.show()
 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 
o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |

In [4]: psi.canonize(10)
Out[4]: <MatrixProductState(tensors=20, structure='I{}', nsites=20)>

In [5]: psi.show()
 2 4 8 10 10 10 10 10 10 10 10 10 10 10 10 10 8 4 2 
>->->->-->-->-->-->-->-->--o--<--<--<--<--<--<-<-<-<
| | | |  |  |  |  |  |  |  |  |  |  |  |  |  | | | |

which means that the norm of the whole state is equivalent to the norm of, here, site 10.

In [6]: psi[10].H @ psi[10]
Out[6]: 1.0000000000000002

This means that when you locally compress the tensor/bond at site 10 you are optimally choosing the best singular values for preserving the norm overall.

This isn't (generally) possible with a PBC MPS:

In [7]: psi = qtn.MPS_rand_state(20, 10, cyclic=True)

In [8]: psi.show()
 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 
+--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--+
   |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |   

In [9]: psi.canonize(10)
Out[9]: <MatrixProductState(tensors=20, structure='I{}', nsites=20)>

In [10]: psi.show()
 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 
+--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--o--+
   |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |   

In [11]: psi[10].H @ psi[10]
Out[11]: 8.392361350641236

This doesn't mean you can't still compress by locally discarding singular values, just that it won't be optimal.

EDIT: just to be a bit clearer, in TEBD, the algorithm tries to move the 'orthogonality' center around with it so that the compression after each gate is applied is optimal.