Update docs index page to reflect new README

docs/src/index.md

@@ -1,5 +1,61 @@
 # PEPSKit.jl
 
+[![docs][docs-dev-img]][docs-dev-url] ![CI][ci-url] [![codecov][codecov-img]][codecov-url]
+
+[docs-dev-img]: https://img.shields.io/badge/docs-dev-blue.svg
+[docs-dev-url]: https://quantumghent.github.io/PEPSKit.jl/dev/
+
+[codecov-img]: https://codecov.io/gh/quantumghent/PEPSKit.jl/branch/master/graph/badge.svg
+[codecov-url]: https://codecov.io/gh/quantumghent/PEPSKit.jl
+
+[ci-url]: https://github.com/quantumghent/PEPSKit.jl/workflows/CI/badge.svg
+
 **Tools for working with projected entangled-pair states**
 
-It contracts, it optimizes, it may be broken at any point.
+It contracts, it optimizes, it may break.
+
+## Installation
+
+The package can be installed through the Julia general registry, via the package manager:
+
+```julia-repl
+pkg> add PEPSKit
+```
+
+## Quickstart
+
+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:
+
+```julia
+using TensorKit, PEPSKit, KrylovKit, OptimKit
+
+# 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)
+
+# 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,
+)
+
+# 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)
+
+@show result.E # -0.6625...
+```