Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity

TL;DR

This paper investigates the near-kernel sector of quantum reduced loop gravity using neural quantum states and variational Monte Carlo, revealing emergent semiclassical structures and distinct classes of solutions.

Contribution

It introduces a novel variational approach with neural quantum states to analyze the near-kernel sector in quantum reduced loop gravity, identifying emergent semiclassical states.

Findings

Near-kernel states organize into three distinct classes.

At high spin cutoffs, two factorized branches emerge.

One branch matches reduced Thiemann coherent states with high fidelity.

Abstract

We study the near-kernel sector of the Hamiltonian constraint operator in the one-vertex model of quantum reduced loop gravity using variational Monte Carlo methods with neural quantum states. The analysis is based on the symmetric Hamiltonian containing both Euclidean and Lorentzian contributions, and on the variational minimization of the positive quadratic operator $\hat{\mathcal Q}=\hat C \hat C^\dagger$ in truncated Hilbert spaces with spin cutoff up to $j_{\mathrm{max}}=1001$. The resulting near-kernel states are found to organize into three qualitatively distinct classes. At low cutoffs, we find solutions that do not factorize across the three edge degrees of freedom. At larger cutoffs, we find two different factorized branches, both described to very high accuracy by products of one-edge wavefunctions but localized in different spin regimes. One of these branches is matched with near-unit fidelity by reduced Thiemann coherent states, providing evidence for an emergent semiclassical organization of the near-kernel sector. The other is likewise strongly factorized, but its one-edge factors are not well described by the same coherent-state family.