Precision Lattice Entanglement Entropy
Methods, convergence, and the universal scaling function
Establishes the area-law coefficient α_s to 0.01% precision via Richardson extrapolation. First lattice extractions of vector and graviton log coefficients, discovering the 50% rule for transverse-traceless modes.
Mar 5, 2026 · Preprint
Plain English
This paper measures the fundamental constants of quantum entanglement on a computer lattice — with enough precision to make or break the dark energy prediction.
The problem
The entanglement entropy framework for the cosmological constant depends on two numbers for each particle species: an area-law coefficient (α) and a logarithmic correction (δ). These numbers must be known to high precision — if α is off by 1%, the dark energy prediction shifts by 1%. Previous lattice calculations lacked the precision and systematic control needed.
The key idea
By using a radial lattice with angular momentum decomposition and Richardson extrapolation, individual lattice artifacts can be systematically removed. The key innovation is the "third difference" method (d3S) which cancels both the dominant area term and subleading corrections, isolating the universal logarithmic coefficient to sub-percent accuracy.
What the paper does
It measures α to 0.01% precision and δ to 0.24% for scalars, vectors, and gravitons. It discovers a "50% rule": transverse-traceless modes carry almost exactly half the entanglement entropy anomaly for both vectors (51.5%) and gravitons (50.8%). It also maps out the full convergence landscape as a function of lattice size and angular cutoff.
Why it matters
These lattice measurements are the numerical foundation for the entire cosmological constant prediction. By achieving sub-percent precision, systematic lattice uncertainties are reduced to a negligible 0.05% contribution to the total error budget — ensuring the 3% gap between prediction and observation is physical, not numerical.
What could go wrong
The fermion area-law coefficient cannot be extracted on the lattice due to UV sensitivity of the Fermi sea — the heat kernel value must be trusted. The lattice regulator breaks conformal invariance, which could introduce scheme-dependent artifacts at subleading order. This is a preprint and has not been peer-reviewed.