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| Format: | Recurso digital |
| Language: | English |
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2026
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| Online Access: | https://doi.org/10.5281/zenodo.20395773 |
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| _version_ | 1866902198957375488 |
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| author | G.H.S.C. Research |
| author_facet | G.H.S.C. Research |
| contents | <pre class="language-markup"><code><p>We present a comprehensive numerical and analytical study of the Hamiltonian constraint spectrum for 2+1D quantum gravity with a positive cosmological constant \( \Lambda \propto 1/k^2 \) on a spatial torus. Using the Turaev-Viro topological quantum field theory formalism at roots of unity \( q = e^{\pi i / (k+2)} \), we exactly diagonalize the Hamiltonian operator on the minimal triangulation (up to \( k=12 \)) and on refined 2×2 and 3×2 periodic lattices (at \( k=3 \) and partially at \( k=4,5 \)). The ground state exhibits the predicted topological degeneracy of \( k+1 \), and we confirm the existence of a non-zero physical excitation gap \( \Delta_{\text{phys}} \) for any finite \( \Lambda \). Statistical scaling analysis demonstrates that the physical gap follows a smooth power-law decay, scaling as \( \Delta_{\text{phys}} \propto \Lambda^{0.895 \pm 0.010} \). Importantly, the asymptotic offset is statistically consistent with zero, meaning the gap vanishes in the flat-space limit \( \Lambda \to 0 \). We therefore characterize this as an <strong>IR-regulated gap</strong> or <strong>curvature-induced gap</strong>, not a fundamental topological mass. Analysis of the spatial wavefunctions reveals that the vacuum state acts as a topological condensate favoring an equilibrium curvature, while the first excited state represents a macroscopic quantum "breathing mode" of the spatial geometry.</p></code></pre> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20395773 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Spectral gap of the Hamiltonian constraint in 2+1D quantum gravity with positive cosmological constant: Numerical Turaev-Viro spectra on the torus G.H.S.C. Research Quantum Gravity Topological Quantum Field Theory TQFT 2+1D Quantum Gravity Turaev-Viro Model Hamiltonian Constraint Exact Diagonalization Numerical Relativity Spectral Gap Cosmological Constant Topological Degeneracy IR-regulated Gap General Relativity and Quantum Cosmology Mathematical Physics <pre class="language-markup"><code><p>We present a comprehensive numerical and analytical study of the Hamiltonian constraint spectrum for 2+1D quantum gravity with a positive cosmological constant \( \Lambda \propto 1/k^2 \) on a spatial torus. Using the Turaev-Viro topological quantum field theory formalism at roots of unity \( q = e^{\pi i / (k+2)} \), we exactly diagonalize the Hamiltonian operator on the minimal triangulation (up to \( k=12 \)) and on refined 2×2 and 3×2 periodic lattices (at \( k=3 \) and partially at \( k=4,5 \)). The ground state exhibits the predicted topological degeneracy of \( k+1 \), and we confirm the existence of a non-zero physical excitation gap \( \Delta_{\text{phys}} \) for any finite \( \Lambda \). Statistical scaling analysis demonstrates that the physical gap follows a smooth power-law decay, scaling as \( \Delta_{\text{phys}} \propto \Lambda^{0.895 \pm 0.010} \). Importantly, the asymptotic offset is statistically consistent with zero, meaning the gap vanishes in the flat-space limit \( \Lambda \to 0 \). We therefore characterize this as an <strong>IR-regulated gap</strong> or <strong>curvature-induced gap</strong>, not a fundamental topological mass. Analysis of the spatial wavefunctions reveals that the vacuum state acts as a topological condensate favoring an equilibrium curvature, while the first excited state represents a macroscopic quantum "breathing mode" of the spatial geometry.</p></code></pre> |
| title | Spectral gap of the Hamiltonian constraint in 2+1D quantum gravity with positive cosmological constant: Numerical Turaev-Viro spectra on the torus |
| topic | Quantum Gravity Topological Quantum Field Theory TQFT 2+1D Quantum Gravity Turaev-Viro Model Hamiltonian Constraint Exact Diagonalization Numerical Relativity Spectral Gap Cosmological Constant Topological Degeneracy IR-regulated Gap General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://doi.org/10.5281/zenodo.20395773 |