Fig. 5: Properties of a quarter-filled SSHH model with OBC under an external magnetic field.
From: Topological phases of a dimerized Fermi–Hubbard model for semiconductor nano-lattices
a Eigenenergy spectrum as a function of the field strength in the non-trivial phase. The levels are colored according to the spin projection Sz of the eigenstates. Only states with positive Sz are considered as the ones with negative Sz rise in energy in a magnetic field, and for each value of Sz the 10 lowest energies are shown. At the critical value \({E}_{B}^{(c)}\approx 0.1\) (indicated by the arrow), the ground state becomes maximally ferromagnetic (with all spins aligned along the field axis) and reduces to the non-interacting limit of the SSH model. b Entanglement entropy between the edges and the bulk for various field strength and Δt. Each contour separates regions where the ground state has different Sz (Sz = 3 indicates the maximally ferromagnetic ground state as there are 6 particles at quarter-filling). At zero field, the entanglement does not drop as Δt changes sign due to the long-range AFM correlation between the edges and the bulk at quarter-filling discussed above. At high field, the system reduces to the SSH model, and the entanglement drops for Δt > 0 due to the formation of the localized edge states, signaling the transition to the non-trivial phase. c Critical field strength at various values of the on-site interaction and hopping amplitude difference. d 1D slices of c for U = 0 (left panel) and Δt = 0.5 (right panel) showing the sharp decrease in the critical field strength with increasing on-site interaction.
