TenNetLib.jl

A Tensor Network Library (TenNetLib.jl) built on top of ITensors.jl for quantum many-body problems.

Build Status	Documentation

The source code for TenNetLib.jl can be found on GitHub.

The documentation for TenNetLib.jl can be found here.

This library requires Julia 1.7+.

TenNetLib.jl features widely-used Tensor Network (TN) codes, designed with a multi-layered abstraction to cater to diverse user needs. The library provides users with varying levels of control over their computations. Currently, TenNetLib.jl presents an array of functionalities for:

• (a) Finite-size Matrix-Product States (MPS): Different variants of Density Matrix Renormalization Group (DMRG) and Time Dependent Variational Principle (TDVP) (including subspace expansion) methods.
• (b) Tree Tensor Network (TTN): Variational search for the ground state and first few excited states.

TenNetLib.jl is registered on Julia General Registry. To install the library (along with ITensors.jl), you can use the following steps:

$ julia

julia> ]

pkg> add ITensors

pkg> add TenNetLib

"Beware of bugs in the above code; I have only proved it correct, not tried it." -- Donald Knuth

If you find bugs or mistakes of any kind, please let us know by adding an issue to the GitHub issue tracker. You are also welcome to submit a pull request.

Here is a list for future additions in the decreasing order of priority. Any help / suggestion is welcome.

• Augmented Tree Tensor Network (aTTN) for variational ground state search for 2D problems.
• Infinite DMRG (iDMRG) and/or Variational Uniform Matrix Product States (VUMPS) to tackle 1D / quasi-1D problems directly at the thermodynamic limit.
• Projected Entangled Pair States (PEPS) for 2D problems.
• Real-time evolution method using PEPS and TTN.

Also, please feel free to ask about a new feature by adding a new request to the GitHub issue tracker labelled feature request. Note that submitting a pull request, providing the needed changes to introduced your requested feature, will speed up the process.

The following code is for a simple DMRG run at the highest level of abstraction without any additional control.

using ITensors
using TenNetLib

let
    N = 32
    sites = siteinds("S=1/2",N)
    os = OpSum()
    
    for j=1:N-1
        os += 1, "Sz", j,"Sz", j+1
        os += 0.5, "S+", j, "S-", j+1
        os += 0.5, "S-", j, "S+", j+1
    end
    
    H = MPO(os,sites)
    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
    psi0 = MPS(sites, states)

    params = DMRGParams(;nsweeps = [5, 5], maxdim = [20, 50],
                        cutoff = 1e-14, noise = 1e-3, noisedecay = 2,
                        disable_noise_after = 3)

    # dmrg2 for two-site DMRG
    en, psi = dmrg2(psi0, H, params)
end

The following code is for a simple TDVP run at the highest level of abstraction without any additional control.

using ITensors
using TenNetLib

let
    N = 32
    sites = siteinds("S=1/2",N)
    os = OpSum()
    
    for j=1:N-1
        os += 1, "Sz", j,"Sz", j+1
        os += 0.5, "S+", j, "S-", j+1
        os += 0.5, "S-", j, "S+", j+1
    end
    
    H = MPO(os,sites)
    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
    psi0 = MPS(sites, states)

    tau = -0.01im    
    engine = TDVPEngine(psi0, H)
    for ii = 1:100

    	# `nsite = "dynamic"` for dynamical selection between
	# single- and two-site variants at different bonds
        tdvpsweep!(engine, tau,
                   nsite = "dynamic";
                   maxdim = 200,
                   cutoff = 1E-12,
                   extendat = 5)

	psi = getpsi(engine)
	# DO STUFF
    end
end

The following code is for a simple TTN ground-state optimzation run at the highest level of abstraction without any additional control. Here we use OpStrings and CouplingModel instead of OpSum and MPO.

using ITensors
using TenNetLib

let
    N = 32
    sites = siteinds("S=1/2",N)
    os = OpStrings()
    
    for j=1:N-1
        os += 1, "Sz" => j,"Sz" => j+1
        os += 0.5, "S+" => j, "S-" => j+1
        os += 0.5, "S-"=> j, "S+" => j+1
    end
    
    H = CouplingModel(os,sites)
    psi0 = TTN(sites, 64, QN("Sz", 0))

    sweeppath = default_sweeppath(psi0)
    
    params = OptimizeParamsTTN(; maxdim = [64, 128], nsweeps = [5, 10], 
                               cutoff = 1e-14, noise = 1e-2, noisedecay = 5, 
                               disable_noise_after = 5)
			       
    en, psi = optimize(psi0, H, params, sweeppath)
end