Entanglement Entropy In Multi-Leg Kitaev Ladders With Interface Defects

The entanglement of different parts of a quantum system is expected to be proportional to the common interface area. Therefore alterations across the interface will lead to changes on the behavior of entanglement entropy. In this work, the effects of bond defects at the boundaries of Kitaev ladders are considered. We find a logarithmic scaling for the ground state entanglement entropy between the two pieces. The prefactor of the logarithm (effective central charge (ECC)) varies continuously with the defect strength. The energy dispersion is also obtained and sharp features in the von Neumann entanglement entropy are observed when bands cross. Phase diagrams for homogeneous Kitaev Hamiltonians with nonzero superconducting paring potential are presented. They show that for chains/legs that are connected to one another through inter-leg hopping, when certain parameters are fine-tuned, the phase transition lines correspond to either single or double gapless modes dispersion. Moreover, even when the defect is turned on, the ECC for ladders with two gapless modes is exactly twice the one for ladders with a single gapless mode. On the other hand, in the absence of superconductivity, we can tune the parameters to obtain homogeneous systems whose number of gapless modes is up to the number of legs of the ladder. Additionally, in this situation, the presence of the bond defect makes the ECC becomes smaller than the number of gapless modes times the ECC of Hamiltonians with one gapless mode. Furthermore, the relationship between the cases with and without superconductivity is presented.