  Quantum spin liquids are exotic quantum phases of matter that do not order
even at zero temperature. While there are several toy models and simple
Hamiltonians that could host a quantum spin liquid as their ground state, it is
very rare to find actual, realistic materials that exhibits their properties.
At the same time, the classical simulation of such instances of strongly
correlated systems is intricate and reliable methods are scarce. In this work,
we investigate the quantum magnet Ca$_{10}$Cr$_7$O$_{28}$ that has recently
been discovered to exhibit properties of a quantum spin liquid in inelastic
neutron scattering experiments. This compound has a distorted bilayer Kagome
lattice crystal structure consisting of Cr$^{5+}$ ions with spin-$1/2$ moments.
Coincidentally, the lattice structure renders a tensor network algorithm in 2D
applicable that can be seen as a new variant of a projected entangled simplex
state algorithm in the thermodynamic limit. In this first numerical
investigation of this material that takes into account genuine quantum
correlations, good agreement with the experimental findings is found. We argue
that this is one of the very first studies of physical materials in the
laboratory with tensor network methods, contributing to uplifting tensor
networks from conceptual tools to methods to describe real two-dimensional
quantum materials.
