Hidden Order in the Heisenberg-Kitaev Ladder
Abstract: String, or hidden order, as it arises in quantum spin systems was first shown to exist in S=1 quantum spin chains that have many experimental realizations. Although the ground-state in such materials looks like a liquid and has no detectable local order parameter, a non-local (string-) order parameter can be defined. Precisely how these ideas can be extended to models in higher dimensions and with spin different from S=1 is not entirely clear and in this talk, I will discuss recent work extending the notion of a string order parameter to S=1/2 ladders. In particular, we study the S=1/2 Kitaev-Heisenberg (KJ) model in two-leg ladders. The Kitaev-Heisenberg model defined on the two-dimensional honeycomb lattice has recently received considerable attention due to possible experimental realizations and our results show that the two-leg ladder very closely models the behavior of the 2D honeycomb lattice. For the Kitaev-Heisenberg ladder, we prove the existence of a non-local string order parameter (SOP) in the Kitaev phase which survives with a finite Heisenberg interaction. This differentiates the Kitaev phases from other nearby phases. Two phases with non-zero SOP corresponding to ferromagnetic and antiferromagnetic Kitaev interactions are identified. The full phase diagram of the KJ model is determined using exact diagonalization and density matrix renormalization group methods, which shows a striking similarity to the KJ model on a two-dimensional honeycomb lattice.
To know more about Prof. Sorensen, you can consult his web page at McMaster University.