Quantum typicality survives non-Abelian gauge constraints: exact analytical prediction confirmed in $SU(2)$ lattice gauge theory

• URL: http://arxiv.org/abs/2606.27402v1
• Date: Wed, 24 Jun 2026 14:18:02 GMT
• Title: Quantum typicality survives non-Abelian gauge constraints: exact analytical prediction confirmed in $SU(2)$ lattice gauge theory
• Abstract summary: We show that quantum typicality, the generic absence of inter-subsystem correlations, persists on the physical Hilbert space of a gauge theory.<n>The Kogut-Susskind Hamiltonian generates correlations from states of definite geometry, while generic states show only regression to the mean.
• Score: 5.559015632900393
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Arguments for emergent spacetime require that quantum typicality, the generic absence of inter-subsystem correlations, persists on the physical Hilbert space of a gauge theory, where non-Abelian constraints could in principle inject geometry-supporting entanglement. Using $SU(2)$ lattice gauge theory on two-dimensional tori ($d_{\mathrm{phys}}$ up to $4{,}193$), we show that it does: the typical mutual information between strictly disjoint links matches an exact parameter-free analytical prediction combining a microcanonical baseline with Haar-random fluctuations. The Kogut-Susskind Hamiltonian generates correlations from states of definite geometry (such as the electric vacuum), while generic states show only regression to the mean, establishing that the arrow of correlation growth requires a non-generic initial condition.

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