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Geometric approach to strongly correlated bosons: From N-representability to the generalized Bose-Einstein condensate force

Chih-Chun Wang and Christian Schilling*

  • *Contact author: c.schilling@lmu.de
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Phys. Rev. B 113, 224511 – Published 8 June, 2026

DOI: https://doi.org/10.1103/v3cy-gx4x

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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Phys. Rev. B 113, 224511– Published 8 June, 2026
  • Received 6 January 2026
  • Revised 30 March 2026
  • Accepted 30 April 2026
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