A set of tools designed to compute entanglement entropy of a MPS.

Because the package isn't registered, please install with

julia> using Pkg; Pkg.add(url="https://github.com/ryanlevy/ITensorEntropyTools.jl")

Consider some MPS p.

The standard way to calculate the entanglement entropy would be a bipartition cut between two regions, which you get from ee_bipartite(p, cut).

However, we generally want to obtain a density matrix of some region of sites. We can do this by tracing out all the sites or if the region is contiguous tracing out the sites leaving the bond or link dimensions. The function ee_region will somewhat automatically determine the best way to do this for you

julia> using ITensorEntropyTools

julia> ee_region(p, [2,3,4]; verbose=true)
Contiguous region found, considering sites and bond versions
Site density matrix would be size (log2) 3.0
Complement sites would be size (log2) 7.0
Bond-based density matrix would be size (log2) 4.0
Using site mode
1.5967236103088644

julia> ee_region(p, [2,3,4,5,6]; verbose=true)
Contiguous region found, considering sites and bond versions
Site density matrix would be size (log2) 5.0
Complement sites would be size (log2) 5.0
Bond-based density matrix would be size (log2) 4.0
Using bond mode
1.6807859305972712

julia> ee_region(p, [1,2,3]; verbose=true)
Using bipartite calculation for region [1, 2, 3]
1.1657496391466677

There is also support for generalized Renyi entropy, in case you don't want von Neumann all the time

julia> ee_region(p, [2,3,4,5,6]; ee_type=EEType("Renyi"),n=0.1)
2.033718897443242

There is support for mutual information between two regions

julia> mutual_info_region(p,[2,3],[5,6])
0.4465377568277278

And tripartite mutual information (multivariate mutual information)

julia> tripartite_ee_region(p,[2,3],[4,5],[6,7])
-0.43954571818905186

This library was written by Ryan Levy, with heavy inspiration from prior work with Abid Khan (@abid1214) with helpful conversations with Bryan K Clark and Edgar Solomonik.

This library has not been rigorously tested so please report any bugs/issues you encounter! PRs and comments are also welcome

• Matrix Free density matrix tools
• Remove dependence on tags
• combine site and link codes?
• Generalized to ITensorNetworks (see network branch)