Tensor network investigation of the double layer Kagome compound Ca₁₀Cr₇O₂₈

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 exhibit 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 Ca₁₀Cr₇O₂₈ 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. Our study contributes to uplifting tensor networks from conceptual tools to methods to describe real two-dimensional quantum materials.