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ITensor / ITensorNetworks.jl

A package with general tools for working with higher-dimensional tensor networks based on ITensor.
MIT License
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BP DMRG - Alpha Version #191

Closed JoeyT1994 closed 3 weeks ago

JoeyT1994 commented 3 weeks ago

This PR adds some files for doing one-site DMRG with belief propagation.

First, support is added in src/beliefpropagationdmrg/tensornetworkoperators.jl for converting an OpSum to a vector of ITensorNetworks which are each trees and span the same set of vertices but have different edges. The sum of those ITensorNetworks is equal to the Hamiltonian represented by OpSum.

Then code is added for doing bp style dmg on those ITensorNetworks in the same vein as alternating update (in the style of using an inserter, extracter and updater)

@mtfishman This is very much a draft for you to look at - it isn't put into the alternating update framework yet because the algorithm is too unstable so I think we still need to figure out some details. In the case the graph g is a tree the code works fine. When it isn't then the code descends in energy well but then tends to "oscillate" near the true ground state energy but is not able to converge to a solution. Moreover, increasing the bond dimension above chi = 2 tends to make things worse.

The BP error on the solution in the example main.jl (periodic ring of 24 sites) is incredibly small (the exact energy from contracting the result vs BP calculated energy agree to ~ 5 d.p.) but the energy oscillations are often on the order of, say, 3 d.p.

emstoudenmire commented 3 weeks ago

A key question about the stability is does the core eigensolver solve a regular or generalized eigenvalue problem?

JoeyT1994 commented 3 weeks ago

The core eigensolver solves a regular eigenvalue problem here by switching to the BP gauge and inserting inverse square roots of the message tensors. This essentially sets the environment for the local state to the identity matrix within the BP approximation.

emstoudenmire commented 3 weeks ago

Thanks. So then the eigensolver part sounds fine. I wonder then if it's the gauging procedure. While mathematically correct, the inverse square roots may cause precision issues. I ran into this in the past when implementing MPS in the "Vidal gauge" for parallel DMRG and it was quite difficult to deal with. I wonder if it's possible to work in a different gauge that avoids any inverses, or else implements the inverses by doing linear solves.