Extending Tensor Network Methods Beyond Pairwise Interactions in Adsorption Systems

Accurate modeling of complex physical systems often requires accounting for many-body interactions. Traditional statistical physics methods, such as Monte Carlo, transfer matrix, cluster approximations, and others, face significant computational challenges. This study introduces a unified tensor algorithm that efficiently incorporates interactions up to the third nearest neighbor. We applied our algorithm to a system of 1,3,5-tris(4-pyridyl)benzene and copper on Au(111). Many-body interactions were considered in two ways: by expressing them through pairwise interactions and by explicitly considering DFT energies for each many-body configuration. This led to both quantitative and qualitative differences in the results. The most significant difference is the lower thermal stability of the "superflower" phase and its subsequent replacement by a disordered structure with higher density. The developed unified tensor algorithm opens up new possibilities for the accurate modeling of complex systems taking into account many-body interactions.