Topological Phase Transition Theory of Strongly Correlated Many Body System

Xavier Plat, Chisa Hotta

Here, the authors show that the entanglement spectrum -- a fingerprint of the quantum many-body wave function -- of strongly correlated fermionic systems can be evaluated almost exactly by density embedding theory. An accurate entanglement spectrum guarantees the accuracy of the local density matrix or the physical properties, and their anomalies generally serve as markers for phase transitions, including not only the Landau symmetry-breaking ones but also topological transitions.

J. W. Clark, VICTOR A. KHODEL, MIKHAIL V. ZVEREV

Alexander Protogenov

J. R. Wen

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.

Wen‐Long You

Peizhi Mai, Jinchao Zhao, Thomas Maier +2 more

We show here two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.