2026/02/28 by Kai Watanabe
Physics and Astronomy · #cond-mat.str-el #cond-mat.mes-hall
We study when a density-matching Kohn--Sham (KS) description can reproduce a many-body Berry phase in a correlated insulator, despite the fact that geometric phases are functionals of the wave function. Focusing on the one-dimensional SSH--Hubbard chain on a ring as a controlled interacting topological model, we introduce a U(1) twist θ (flux insertion). The many-body ground state along the full twist cycle is computed by the density-matrix renormalization group (DMRG), while the onsite interaction U is tuned from the noninteracting to the strong-coupling regime. At half filling in the inversion-symmetric gapped regime, our DMRG calculations show that the density remains constant within numerical accuracy over the entire (θ,U) range studied. Thus, the density has no dependence on either the flux θ or the interaction strength U. Accordingly, the symmetry-preserving density constraint collapses the KS reference to an SSH-type quadratic representative with U-independent geometric diagnostics. Nevertheless, the many-body wave function exhibits a nontrivial geometric response: the quantum metric associated with the θ-parametrized ground-state manifold depends on θ at intermediate U and is strongly suppressed at large U, consistent with the charge fluctuation freezing. Intriguingly, the KS and many-body Berry phases coincide throughout the gapped regime as U is tuned from weak to strong coupling. We show that this agreement is best understood as symmetry-enforced ℤ2 sector matching, rather than as evidence that the density encodes the many-body Berry connection.