MERA.jl provides Julia implementations of some basic Multiscale Entaglement Renormalization Ansatz algorithms. It only implements infinite, translation invariant MERAs. At the moment it has implementations of both ternary and binary MERAs, with functions for doing energy minimization, evaluating local expectation values, and computing scaling dimensions.
MERA.jl makes extensive use of TensorKit, and uses it to support global internal symmetries, both Abelian and non-Abelian.
MERA.jl remains in active development as of January 2020. Some further plans include supporting modified binary MERAs, improving performance, and developing the optimization method.
The folder demo has a script demo.jl, that runs energy minimization on either the Ising or the XXZ model (your choice), and computes scaling dimensions and entanglement entropies from the resulting MERA. The best way to get going is to clone this repo, navigate to its folder, open a Julia prompt and do
]activate .
include("demo/demo.jl")
demo.jl writes to disk the MERAs it creates, by default in a folder called JLMdata. Another script, demo/demo_refine.jl, can be used to load these files, optimize the MERA further for better convergence, and write them back to disk. If I would need high quality results for a given bond dimension, I would first generate a decent starting point using demo.jl, which builds the MERA up by slowly increasing bond dimension, and then use demo_refine.jl to push for proper convergence. Both of these scripts use demo/demo_tools.jl, which deals with creating Hamiltonians, writing to and reading from disk, and gradually increasing bond dimension during an optimization.
The actual library is obviously in src. The type system is based on a an abstract type GenericMERA{T} where T <: Layer, and its concrete subtypes TernaryMERA = GenericMERA{TernaryLayer} and BinaryMERA = GenericMERA{BinaryLayer}. The file src/genericmera.jl implements functions that are independent of the exact type of MERA. src/ternarylayer.jl and src/binarylayer.jl provide the details of things like ascending/descending superoperators, that depend on the specific MERA. src/tensortools.jl supplies some functions for TensorKit objects such as TensorMaps and vector spaces that the rest of the package needs.