Topological Phase Transition Properties of Interacting Bose-Einstein Condensates in Quasi-Periodic Potential Wells

Topological state characterization in interacting quasi-periodic systems remains challenging because conventional band-topology approaches become invalid in the presence of strong many-body correlations and broken translational symmetry. This study develops a generalized many-body Zak phase framework for investigating topological phase transitions in Bose–Einstein condensates confined within quasi-periodic potential wells. By introducing a quasimomentum manifold derived from quasi-periodic phase symmetry and constructing gauge-continuous ground-state families, topological invariants are directly extracted from many-body wavefunctions without relying on Bloch bands, Brillouin zones, or bulk energy gaps. The proposed approach is integrated with density matrix renormalization group calculations to establish a unified characterization of superfluid, localized, and critical regimes. Results show that a stable topologically nontrivial phase emerges at U/J = 3.2 and ∆/J = 2.8, where the momentum distribution exhibits symmetric peaks at k = ±π/2 with an amplitude of 1.87. Open-boundary analysis reveals strongly localized edge modes with approximately 90% density concentration near system boundaries, while the entanglement spectrum displays a symmetry-protected doubly degenerate structure. The results demonstrate that interaction and quasi-periodicity jointly stabilize nontrivial topological states and associated wave-localization phenomena. The proposed framework provides a rigorous methodology for analyzing topological phase evolution, geometric-phase transitions, and wave propagation characteristics in strongly correlated quasi-periodic systems.