Variance of purified MPS state

How do I use this algorithm? What does that parameter do?
Post Reply
Leyin
Posts: 2
Joined: 11 Sep 2024, 12:36

Variance of purified MPS state

Post by Leyin »

Hi there,

I am currently using TenPy to try to calculate thermodynamic observables for bigger yet finite systems. For the first test I wanted to do some smaller ones to test all tools. There I noticed that the MPO.variance method does not work for "non standard MPS" I checked the code and saw the exception case.
My question is now , is there a workaround that can handle that , just as for example constructing a H**2 and calculate it with MPO.expectation or similiar without requring to rewrite complete bases of classes?
Already thanks in advance for any help that might come!
User avatar
Johannes
Site Admin
Posts: 457
Joined: 21 Jul 2018, 12:52
Location: TU Munich

Re: Variance of purified MPS state

Post by Johannes »

It's not hard to generalize and adjust the source of that variance function to work with purificationMPS - all you need to do is to initially check whether you have the additional q leg (at the top of the function), and if so, in addition contract the additional ['q'] with ['q*'] leg in the tensordot where you "close" one column, i.e. the tensordots of contr with th.conj() and B.conj(), respectively.
Leyin
Posts: 2
Joined: 11 Sep 2024, 12:36

Re: Variance of purified MPS state

Post by Leyin »

Ah okay so for example for the 0 site i would add

Python: Select all

contr = npc.tensordot(contr, contr, axes=[   'q', 'q*'   ])  
in addition to the previos p leg contraction and same further on for B ?

Since the contraciton with the W's only happens on the physical legs p and all that gets added new are the virtual legs q and q* on top and bottom of the B - MPS right?

Or is it smarter to do it together with

Python: Select all

contr = npc.tensordot(contr, B.conj(), axes=[['vR*', 'p' , 'q'], ['vL*', 'p*, 'q*']]) 
not sure how much of a different in calculation time it would be
Post Reply