Tensor network construction for lattice gas models: Hard-core and triangular lattice models

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.

Critical line of the triangular Ising antiferromagnet in a field from a C_{3}-symmetric corner transfer matrix algorithm

The corner transfer matrix renormalization group (CTMRG) algorithm has been extensively used to investigate both classical and quantum two-dimensional (2D) lattice models. The convergence of the algorithm can strongly vary from model to model depending on the underlying geometry and symmetries, and the presence of algebraic correlations. An important factor in the convergence of the algorithm is the lattice symmetry, which can be broken due to the necessity of mapping the problem onto the square lattice. We propose a variant of the CTMRG algorithm, designed for models with C_{3}-symmetry, which we apply to the conceptually simple yet numerically challenging problem of the triangular lattice Ising antiferromagnet in a field, at zero and low temperatures. We study how the finite-temperature three-state Potts critical line in this model approaches the ground-state Kosterlitz-Thouless transition driven by a reduced field (h/T). In this particular instance, we show that the C_{3}-symmetric CTMRG leads to much more precise results than both existing results from exact diagonalization of transfer matrices and Monte Carlo.