MERA.jl
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 ternary, binary, and modified binary MERAs, with functions for doing energy minimization, evaluating local expectation values, and computing scaling dimensions. An implementation is provided of the classic alternating energy minimization algorithm, that in the code is called the Evenbly-Vidal, or EV, algorithm. Work is also ongoing on gradient based optimization methods. 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 April 2020.
Usage
The folder demo has a script demo.jl, that runs energy minimization on either the Ising or the XXZ model, 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. You can for instance first create a decent decent starting point for a MERA using demo.jl, since it 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. Both demo.jl and demo_refine.jl take plenty of command line arguments, allowing things
julia --project=. demo/demo.jl --model=XXZ --meratype=binary --chi=5 --layers=4 --symmetry=none
See the source code for more details.
The actual library is obviously in src. The type system is based on an abstract type GenericMERA{T} where T <: Layer, and its concrete subtypes such as TernaryMERA = GenericMERA{TernaryLayer} and BinaryMERA = GenericMERA{BinaryLayer}. The file src/genericmera.jl implements functions that are independent of the exact type of MERA. src/simplelayer.jl implements methods for the abstract type SimpleLayer that all the concrete Layer types are subtypes of, that just assumes that each layer consists of a finite number of TensorMaps. src/ternarylayer.jl, src/binarylayer.jl, and src/modifiedbinarylayer.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.