Mid-plateau State as a Topological Phase in Dimerized Spin-1/2 Two-Leg Ladders

The spin-1/2 two-leg ladders with dominant spatially modulated rung exchanges are known as the dimerized ladders. In the limit of strong rung exchange, the ground state of the system is in the rung-singlet (RS) gapped phase. Applying an external magnetic field creates two additional new gapped phases in the ground-state phase diagram of the model beside the existence of the two trivial gapless Luttinger liquid (LL) phases. It is already specified that the magnetization curve of the system exhibits a plateau at magnetization which is equal to the half of the saturation value in one of the non-trivial gapped phases known as the mid-plateau state. Here, we calculate the entanglement entropy and entanglement spectrum (ES) for finite ladder systems using the numerical Lanczos method. In fact, it has been suggested that the topological properties of the ground state can be reflected by specific degeneracy of the ES. We investigate the gapped RS and the mid-plateau phases where our outcomes show even degeneracy in the ES in the non-trivial RS and mid-plateau gapped phases is an indication of the symmetry-protected topological phases. In addition, we argue about the difference between the results of ES for various divisions of the ladder system.