Thermodynamic Properties of Polar Molecules in Optical Lattices Using the Bose Hubbard Model with Local Three Body Interactions

Over the past two decades, cold atoms in optical lattices have emerged as a versatile platform for studying quantum many-body systems, particularly through the Bose-Hubbard Model (BHM). While the conventional BHM has been effective in describing the superfluid–Mott insulator (SF–MI) transition in systems with two-body interactions, it fails to account for local three-body interactions at zero temperature, especially in polar molecules with long-range dipolar forces. Two body interactions defined as acts when, the collisions are short range and due to dipole-dipole attraction. On the other hand, three body interactions defined as act when and are effective higher order processes which are virtual excitations and an harmonic. The three body term, suppresses high onsite energy occupancy and reduces the potential of the onsite number distribution lowering entropy at fixed. This study extends the BHM to incorporate local three- body interactions and investigates the thermodynamic behavior of polar molecules in optical lattices. The Hamiltonian was formulated in second quantization, diagonalized using Fourier transformation, and thermodynamic quantities including specific heat capacity, Sommerfeld coefficient, internal energy, partition function, and entropy were derived and analyzed computationally using Mathcad. The results reveal that three-body interactions substantially modify the energy spectrum and phase boundaries of the system. The specific heat capacity exhibited a prominent peak at 5.2 K, confirming a second-order SF–MI phase transition. The Sommerfeld coefficient peaked at 11.1 K (0.001121 J/Kg. K), highlighting enhanced fermionic contributions near the Fermi surface. Internal energy rose rapidly between 0–20 K, indicating strong quantum fluctuations, before plateauing around 0.98 J at higher temperatures. The partition function displayed an exponential increase with temperature, reflecting enhanced state degeneracy under three-body interactions. Entropy rose sharply below 30 K, marking the transition from ordered superfluid to disordered normal phases, and reached a maximum near 115 K, indicating thermal equilibrium. These findings confirm that three-body interactions play a decisive role in shaping the thermodynamic properties and critical behavior of strongly correlated bosonic systems. Beyond advancing theoretical understanding of SF–MI transitions, this work offers insights relevant to high-temperature superconductivity, quantum information processing, magnetic heterostructures, and nanoelectronic device development.