Twice Hidden Order in the Kitaev-Gamma Ladder

Today, there is a growing class of Kitaev materials where it is believed that bond-dependent Kitaev interactions are present. However, other interactions are also often present, among them the so-called Gamma (Γ) term and here we consider the Kitaev-Gamma (KG) model. In order to obtain highly accurate results it is often useful to restrict the analysis to low-dimensions and in this talk we mainly discuss the ladder. Using matrix product states it is possible to determine the phase-diagram of this ladder system with very high precision including the effects of a magnetic field in the [111] direction. An abundance of new phases appear. Here we focus on one of them, dominated by the antiferromagnetic Gamma point where it can be shown that twice hidden order is present in the sense that there exists a unitrary mapping to another model which has long-range string order.