Exact solution to a class of generalized Kitaev spin-1/2 models in arbitrary dimensions

Abstract

We construct a class of exactly solvable generalized Kitaev spin-1/2 models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An exactly solvable quantum spin-1/2 models can be mapped to a gas of free Majorana fermions coupled to static Z2 gauge fields. We classify these exactly solvable models according to their parent models. Any model belonging to this class can be generated by one of the parent models. For illustration, a two dimensional (2D) tetragon-octagon model and a three dimensional (3D) xy bond model are studied.

Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

“…The JW string is defined so that the odd sites belongs to the • sublattice and the even ones are the • sublattice. Obviously, this model is a spin 1/2 model fulfilling the requirements stated in [40] and thus another example of Kitaev-inspired model. By the Jordan-Wigner transformation, we have that…”

“…Because of the generality of the exact solution procedures for the Kitaev-inspired models, the methods presented here can be readily applied to other Kitaev-inspired models. These include, for example, the generalizations of the original Kitaev honeycomb model to different lattices [16-19, 27, 34], different dimensions [20,23,24,[38][39][40], and higher spins [26,29]. In the Appendix D, one additional example of applying our approach to the 1D BCS-Hubbard model is provided.…”

Grüneisen ratio quest for self-duality of quantum criticality in a spin-1/2 XY chain with Dzyaloshinskii–Moriya interaction

“…Note that δ=0 is the self-dual QCP separating the topological phases. Nevertheless, the duality is not a unitary transformation [37]. Near the QCP, the GR as a function of δ under different temperatures is plotted in figure 2 As a magnetic field is turned on, it brings to plentiful QPTs.…”

“…In the absence of magnetic field, the quantum critical lines by gap closing that separate the gapped topological and gapless TLL phases are identified, in which the topological to topological transition depends on the anisotropy parameter associated with a self-dual QCP, while the QCP signaling the transition from topological to TLL depends on the DM interaction without self-duality, implying a general QPT. As a magnetic field is turned on, when the DM interaction is weaker than the anisotropy parameter, the transverse-field Ising terms predominate, implying that the self-duality at a QCP is Z 2 symmetry acting on the magnetic field [9,14,15,36,37]. Otherwise, the strong DM interaction will break the self-dual symmetry and lead to a general QPT into the TLL phase.…”

Lacing topological orders in two dimensions: Exactly solvable models for Kitaev's sixteen-fold way

“…[22][23][24][25][26][27][28][29], respectively. There are also some generalized models with multiple-spin interactions [30,31]. The generalizations to higher spin models have been achieved in a Γ matrix representation [32][33][34][35].…”