Topological phases of the Kitaev-Hubbard model at half filling

Abstract

The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping t and spin-dependent hopping t . We study this model in the weak to intermediate coupling regime, at half-filling, using the Cellular Dynamical Impurity Approximation (CDIA), an approach related to Dynamical Mean Field Theory but based on Potthoff's variational principle. We identify four phases in the (U, t ) plane: two semi-metallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems. arXiv:1506.00501v1 [cond-mat.str-el] 1 Jun 2015

Kitaev honeycomb tensor networks: Exact unitary circuits and applications

“…The case of non-bipartite lattices would be particularly interesting, since timereversal symmetry could be spontanously broken in such cases, thus leading to chiral ground states without the need of adding external magnetic fields [14,56]. Moreover, our results can also be a good starting point for numerical simulations of, e.g., Kitaev-Heisenberg [18] and Kitaev-Hubbard [19] models with exotic TN structures. A similar 3d TN construction is also expected for the case of adding a 3-spin interaction to the model, which opens a gap and keeps the exact solvability.…”

“…These results make this model a paradigmatic example to study abelian, nonabelian, chiral, and non-chiral topological phases, as well as quantum phase transitions between them, in a fully analytic way. Moreover, from the experimental point of view the model is relevant in the study of some materials, where one needs to consider also the presence of competing Heisenberg and/or Hubbard interactions [18,19]. Such Hamiltonians are dubbed "Kitaev-Heisenberg" and "Kitaev-Hubbard" models, and since they are no longer exactly solvable, they have been the subject of several numerical studies in recent years.…”

Quantum cluster approach to the spinful Haldane-Hubbard model

“…As mentioned earlier, studies of models of interacting fermions where explicitly broken time-reversal and/or particle-hole symmetries preclude the use of powerful QMC methods are notoriously hard. Besides VCA and CDMFT however, other powerful numerical methods have been successfully applied recently to the study of models of correlated Chern insulators, such as the cellular dynamical impurity approximation 84 (CDIA) and DMRG. 85,86 It would be worthwhile to apply these methods to the study of the spinful HH model at half filling.…”

Distinct-symmetry spin-liquid states and phase diagram of the Kitaev-Hubbard model

“…This model, which we call a Kitaev-Hubbard model, was introduced by Duan et al, and can be realized in cold atom systems [32][33][34] , has been studied numerically at quarter filling 35 and half filling 36,37 . Our motivation is that as a function of t ′ /t, this model interpolates between the usual Hubbard model at t ′ /t = 0 and 1 where the Kitaev Z 2 SL…”