Tensor networks for hierarchical lattices

Abstract

In this paper, we propose an approach to obtain numerically exact solutions for hierarchical lattices by representing them as a tensor network. The visual representation of these networks greatly simplifies the computational algorithm. Furthermore, we introduce a method for incorporating single-node interactions, enabling us to disregard the inhomogeneity of the hierarchical lattice nodes and simulate the behavior on a regular lattice instead. This methodology allows for qualitative studies of the phase space of desired lattice models with single-node interactions, which holds relevance for adsorption systems. The efficiency of the approach is demonstrated using the Ising model and the binary gas adsorption model as examples.