A Geometric Approach to Strongly Correlated Bosons: From $N$-Representability to the Generalized BEC Force

• URL: http://arxiv.org/abs/2601.01652v1
• Date: Sun, 04 Jan 2026 20:10:59 GMT
• Title: A Geometric Approach to Strongly Correlated Bosons: From $N$-Representability to the Generalized BEC Force
• Authors: Chih-Chun Wang, Christian Schilling,
• Abstract summary: Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons.<n>We first establish that translational symmetry, together with a fixed pair interaction, enables an exact functional formulation expressed solely in terms of momentum occupation numbers.
• Score: 12.368400057425
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons. We first establish that translational symmetry, together with a fixed pair interaction, enables an exact functional formulation expressed solely in terms of momentum occupation numbers. Employing the constrained-search formalism and exploiting a geometric correspondence between $N$-boson configuration states and their one-particle reduced density matrices, we derive the general form of the ground-state functional. Its structure highlights the omnipresent significance of one-body $N$-representability: (i) the domain is exactly determined by the $N$-representability conditions; (ii) at its boundary, the gradient of the functional diverges repulsively, thereby generalizing the recently discovered Bose-Einstein condensate (BEC) force; and (iii) an explicit expression for this boundary force follows directly from geometric arguments. These key results are demonstrated analytically for few-site lattice systems, and we illustrate the broader significance of our functional form in defining a systematic hierarchy of functional approximations.

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