solvers.md

Solvers

ITensorNetworks.jl provides sweep-based solvers for variational problems on tree tensor networks. All solvers follow the same high-level pattern:

1. Start from an initial ITensorNetwork guess.
2. Sweep over the network, solving a small local problem at each site or pair of sites.
3. After each local solve, truncate the updated bond to control bond dimension growth.
4. Repeat for nsweeps sweeps.

Eigenvalue Problems — eigsolve / dmrg

[eigsolve](@ref ITensorNetworks.eigsolve) finds the lowest eigenvalue and corresponding eigenvector of an operator (e.g. a Hamiltonian) using a DMRG-like variational sweep algorithm. [dmrg](@ref ITensorNetworks.dmrg) is an alias for eigsolve.

using Graphs: vertices
using ITensorNetworks: ITensorNetwork, dmrg, dst, edges, normalize, siteinds, src, ttn
using ITensors: Index, OpSum, random_itensor
using NamedGraphs.GraphsExtensions: incident_edges
using NamedGraphs.NamedGraphGenerators: named_comb_tree

function random_state(g, s; link_space)
    l = Dict(e => Index(link_space, "Link") for e in edges(g))
    l = merge(l, Dict(reverse(e) => l[e] for e in edges(g)))
    ts = Dict(
        v => random_itensor(only(s[v]), (l[e] for e in incident_edges(g, v))...)
            for v in vertices(g)
    )
    return ITensorNetwork(ts)
end

# Build a Heisenberg Hamiltonian on a comb tree
g = named_comb_tree((3, 2))
s = siteinds("S=1/2", g)
H = let h = OpSum()
    for e in edges(g)
        h += 0.5, "S+", src(e), "S-", dst(e)
        h += 0.5, "S-", src(e), "S+", dst(e)
        h += "Sz", src(e), "Sz", dst(e)
    end
    ttn(h, s)
end

# Random initial state (normalise first!)
psi0 = normalize(ttn(random_state(g, s; link_space = 2)))

# Run DMRG
energy, psi = dmrg(H, psi0;
    nsweeps = 2,
    nsites = 2,
    factorize_kwargs = (; cutoff = 1e-10, maxdim = 10),
    outputlevel = 1,
)

ITensorNetworks.eigsolve
ITensorNetworks.dmrg

Time Evolution — time_evolve

ITensorNetworks.time_evolve