Connectivity Engineering: Topological Frustration in Spin Networks, Ground State Energy Truncation, and Dark Energy Analogy

There is a huge discrepancy between the divergent vacuum zero-point energy in quantum field theory and the macroscopic cosmological constant. Within the framework of connectivity engineering, this paper explores the regulatory mechanism of underlying graph topology on the ground state energy of finite systems. By introducing a truncated step k in a one-dimensional XXZ spin network, numerical results show that the absolute value of the system's ground state energy does not decline trivially and linearly with the reduction of interaction bonds, but rather exhibits strong non-trivial topological frustration. The normal network (k=1), due to strong local entanglement, exhibits a lower bare ground state energy density; while after introducing long-range geometric decoupling, the parity matching of sub-chain lengths and boundary reconstruction lead to a non-monotonic evolution of the ground state energy density, reaching a maximum at k=4 due to odd-lattice frustration. This topology-induced energy renormalization conceptually provides a minimal discrete sandbox for the "geometric truncation" of vacuum energy, and implies that the residual energy of macroscopic spacetime (dark energy) may correspond to the geometric frustration tension of the underlying discrete network that has not been fully canceled after topological saturation.