whether the density matrix is similar to a low or high temperature one. I think it's actually an open topic of research, and there may need to be different algorithms for different cases like e.g. In general, I don't know of an efficient way to get the von Neumann entropy for a subregion A described by a density matrix in the form of an MPO. So if you could use the second Renyi entropy instead of von Neumann entropy I could tell you more about how to obtain that from an MPO including drawing some diagrams to show you the idea. Given an MPO as a starting point, representing a density matrix, it's straightforward to compute the second Renyi entropy of a subregion A consisting of sites 1.N_A. So I can think of 3 ways to proceed or ways to approach this (I'd recommend #1 if applicable): I don't know how to select the eigenvalues of a sector (the physical sector corresponding to the projection of the density matrix in the subspace with fixed number of bosons), from a theoretical point of view. In the case of the density matrix, after the outer product the indices contain bot positive and negative q's, because they should be corresponding to the QN flux, namely how much a given block changes the quantum number when acting on an MPS. I seem not to find the results I expect and that I get using ED (Exact Diagonalization).Īssuming to have a bosonic site, using an SVD on MPS I can get then singular values corresponding to QN("Nb",q) where q is the fixed number of bosons, just working on the index of the tensor. Unfortunately I already did what you said, but I'm not quite sure how to handle the indices and extract the eigenvalues corresponding to a given QN sector. I am sorry to hear that you assume I didn't check the documentation. I'm using Julia, I should have said that. The Tensor Decompositions page is also the first thing to show up in the specialized Google search when I typed "density matrix diagonalization." For instance, looking at the In-Depth Documentation page ( ), the Tensor Decompositions link mentions density matrix diagonalization in the brief description next to it. It'll save you some waiting time if you check the documentation before posting a question. There are examples in that page for both. I've used the diagHermitian with good success, but there is also a denmatDecomp that is worth looking at. Since the density matrix is an Hermitian matrix, you can use the Tensor Decompositions for matrices rather than MPSs ( ). Assuming you're using the C++ version (else, look for the same stuff mentioned below but here: )įor the first case, note that your psi isn't normalized when you do \sum_, so you might want to normalize that (I don't think it's done automatically, but that's straight-forward for you to calculate, for the function to normalize an MPS, look at the section on the Functions for Modifying an MPS here: ).
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |