[14]Connectivity Engineering: Topological Frustration in Spin Networks, Ground State Energy Truncation, and Dark Energy Analogy
- 1Independent Researcher
Abstract
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.
Related
- [15]Connectivity Engineering: Topological Enhancement of Quantum Entanglement Structure and Generalized Area Law by Fractal Geometry
- [16]Connectivity Engineering: Irreversible Entropy Accumulation Induced by Topological Quenching and the Arrow of Time
- Frustration-Free Models for Topological Holography: Fusion Spin Chains as Boundary Algebras
- Topological spin textures in 2D altermagnetic chromium chalcogenides: Interplay between magnetic frustration and Dzyaloshinskii-Moriya interaction
- [01]Connectivity Engineering: Deterministic Geometric Decoupling and Internal Entanglement Dynamics
BibTeX
@misc{luo202614connectivity,
title = {{[14]Connectivity Engineering: Topological Frustration in Spin Networks, Ground State Energy Truncation, and Dark Energy Analogy}},
author = {Wenjun Luo},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23665349},
url = {https://zenodo.org/records/23665349},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - [14]Connectivity Engineering: Topological Frustration in Spin Networks, Ground State Energy Truncation, and Dark Energy Analogy
AU - Wenjun Luo
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23665349
UR - https://zenodo.org/records/23665349
AB - 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.
ER -