Technological University Team Presents Exact Influence Functional for Entanglement Analysis
Babatunde Moses Ayeni, from Technological University Dublin, in collaboration with Maynooth University, details an exact lattice formulation revealing how complex quantum systems transition towards simpler, Gaussian behaviours. Ayeni and colleagues present a new analysis of a two-leg hard-core ladder, showing its reduced state factorises into predictable components. The analysis offers a controlled and closed-form framework detailing the evolution from highly non-Gaussian lattice states to their quadratic continuum form during coarse-graining, representing a fundamental advancement beyond traditional top-down approaches to understanding low-dimensional quantum systems and the emergence of Gaussian entanglement theory. Lattice simplification via factorisation of reduced states during coarse-graining A controlled, closed-form framework demonstrates how highly non-Gaussian lattice states evolve towards a quadratic continuum form under coarse-graining, suppressing higher-order corrections to a degree exceeding previous analytical capabilities. Traditional analytical methods, such as bosonization and Luttinger-liquid theory, often begin with the long-wavelength degrees of freedom, effectively bypassing a detailed understanding of how lattice-scale, non-Gaussian correlations are lost during the coarse-graining process. This new formulation addresses this limitation by starting directly from the underlying lattice structure, providing a pathway to understand the simplification of complex quantum systems. By constructing an exact lattice influence-functional representation for a two-leg hard-core ladder, the reduced state factorises into a product-state amplitude and a full-counting-statistics functional, offering a stronger foundation for effective field theories and a more transparent connection between microscopic lattice details and macroscopic effective descriptions. The reduced state of a two-leg hard-core ladder factorises into predictable components: a product-state
