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# PEPSKit.jl | ||
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[![docs][docs-dev-img]][docs-dev-url] ![CI][ci-url] [![codecov][codecov-img]][codecov-url] | ||
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[docs-dev-img]: https://img.shields.io/badge/docs-dev-blue.svg | ||
[docs-dev-url]: https://quantumghent.github.io/PEPSKit.jl/dev/ | ||
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[codecov-img]: https://codecov.io/gh/quantumghent/PEPSKit.jl/branch/master/graph/badge.svg | ||
[codecov-url]: https://codecov.io/gh/quantumghent/PEPSKit.jl | ||
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[ci-url]: https://github.com/quantumghent/PEPSKit.jl/workflows/CI/badge.svg | ||
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**Tools for working with projected entangled-pair states** | ||
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It contracts, it optimizes, it may be broken at any point. | ||
It contracts, it optimizes, it may break. | ||
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## Installation | ||
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The package can be installed through the Julia general registry, via the package manager: | ||
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```julia-repl | ||
pkg> add PEPSKit | ||
``` | ||
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## Quickstart | ||
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After following the installation process, it should now be possible to load the packages and start simulating. | ||
For example, in order to obtain the groundstate of the 2D Heisenberg model, we can use the following code: | ||
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```julia | ||
using TensorKit, PEPSKit, KrylovKit, OptimKit | ||
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# constructing the Hamiltonian: | ||
Jx, Jy, Jz = (-1, 1, -1) # sublattice rotation to obtain single-site unit cell | ||
physical_space = ComplexSpace(2) | ||
T = ComplexF64 | ||
σx = TensorMap(T[0 1; 1 0], physical_space, physical_space) | ||
σy = TensorMap(T[0 im; -im 0], physical_space, physical_space) | ||
σz = TensorMap(T[1 0; 0 -1], physical_space, physical_space) | ||
H = (Jx * σx ⊗ σx) + (Jy * σy ⊗ σy) + (Jz * σz ⊗ σz) | ||
Heisenberg_hamiltonian = NLocalOperator{NearestNeighbor}(H / 4) | ||
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# configuring the parameters | ||
D = 2 | ||
chi = 20 | ||
ctm_alg = CTMRG(; trscheme = truncdim(chi), tol=1e-20, miniter=4, maxiter=100, verbosity=1) | ||
opt_alg = PEPSOptimize(; | ||
boundary_alg=ctm_alg, | ||
optimizer=LBFGS(4; maxiter=100, gradtol=1e-4, verbosity=2), | ||
gradient_alg=GMRES(; tol=1e-6, maxiter=100), | ||
reuse_env=true, | ||
verbosity=2, | ||
) | ||
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# ground state search | ||
state = InfinitePEPS(2, D) | ||
ctm = leading_boundary(CTMRGEnv(state; Venv=ComplexSpace(chi)), state, ctm_alg) | ||
result = fixedpoint(state, Heisenberg_hamiltonian, opt_alg, ctm) | ||
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@show result.E # -0.6625... | ||
``` |