A few questions about MPS class, PBC, and dmrg

Question

Hi Miles,

If it is not much of a problem, can you please clarify some of my questions regarding ITensor library.

(1) The MPS class has orthogonalize() member function to bring it in right canonized form (except site 1), but the algorithm is unfamiliar. I have searched papers for this algorithm, but couldn't find it. Can you please explain the algorithm? And how is it different from canonization by svd? It is definitely faster than the svd method.

(2) How do I ensure PBC for a MPS ? If I manually create an MPO with first and last term as matrices, and not as row or column vectors, will the dmrg method result a MPS with PBC? I have checked the code for sum, but could not find a PBC version of it.

(3) dmrg function is the usual two-site dmrg method. Is there any provision for single-site dmrg?

with regards,
Titas

Answer 1

Hi Titas,
1. The algorithm hasn’t been formally published anywhere yet, but is discussed in words sometimes in various papers (not enough for most people to know of it of course. Here is a link to a new website I’m working on which describes this and other algorithms:
http://tensornetwork.org/mps/index.html#compression

1. I don’t recommend using periodic MPS. No efficient and/or reliable algorithms are known for them, basically. For most purposes you can use finite open-boundary or infinite algorithms. Here is an article I wrote about it:
   http://itensor.org/docs.cgi?page=articles/periodic

2. Yes we are planning to add single site DMRG but don’t have support for it yet.

Best regards, Miles

Comments

Many thanks!!!