Exact Leg-Cut Influence Functional and Emergence of Gaussian Entanglement Theory in a Statistical-Dressing Ladder Model

• URL: http://arxiv.org/abs/2606.25669v1
• Date: Wed, 24 Jun 2026 10:29:12 GMT
• Title: Exact Leg-Cut Influence Functional and Emergence of Gaussian Entanglement Theory in a Statistical-Dressing Ladder Model
• Abstract summary: We present an exact lattice formulation showing how non-Gaussian lattice-scale correlations are discarded under coarse-graining.<n>We show how highly non-Gaussian lattice states evolve toward their quadratic continuum form under coarse-graining.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The emergence of Gaussian effective field theories in low-dimensional quantum systems is traditionally understood through top-down frameworks such as bosonization and Luttinger-liquid theory. However, these approaches typically focus on the long-wavelength degrees of freedom in ways that do not directly track how non-Gaussian lattice-scale correlations are progressively discarded under coarse-graining. In this work, we present an exact lattice formulation from which this phenomenon emerges analytically. We analyze a two-leg hard-core ladder under a leg bipartition, where non-local statistical strings cross the entanglement cut. We construct an exact lattice influence-functional representation showing that the reduced state factorizes strictly into a product-state amplitude and a full-counting-statistics functional. By introducing a commuting linked-cluster superoperator hierarchy that bypasses Baker-Campbell-Hausdorff ordering ambiguities, we prove that the first mixedness-generating sector is strictly density-density in character. Under a specific systematic coarse-graining procedure, we analytically derive the suppression of higher-order corrections, providing a controlled, closed-form framework showing how highly non-Gaussian lattice states evolve toward their quadratic continuum form under coarse-graining. We corroborate these analytical predictions through finite-size exact diagonalization and entanglement-spectrum diagnostics.

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