We study the double-exchange model at half-filling with competing superexchange interactions on a triangular lattice, combining exact diagonalization and Monte Carlo methods. We find that in between the expected itinerant ferromagnetic and 120° Yafet-Kittel phases a robust scalar-chiral, insulating spin state emerges. At finite temperatures the ferromagnet-scalar-chiral quantum critical point is characterized by anomalous bad-metal behavior in charge transport as observed in frustrated itinerant magnets R2Mo2O7.

We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time τN ∼ N 4 . This limits achievable sizes to N ∼ 100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size Nc, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method τN,N c ∼ N N 3 c . Our results are obviously exact when Nc = N , and converge quickly to this asymptote with increasing Nc. The accuracy improves in systems where the effective disorder seen by the fermions is large. We provide results of preliminary calculations on the Holstein model and the Double Exchange model. The 'locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control.

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We establish that the interplay of itinerant fermions with localized magnetic moments on a checkerboard lattice leads to magnetic flux-phases. For weak itineracy the flux-phase is coplanar and the electronic dispersion takes the shape of graphene-like Dirac fermions. Stronger itineracy drives the formation of a non-coplanar, chiral flux-phase, in which the Dirac fermions acquire a topological mass that is proportional to a ferromagnetic spin polarization. Consequently the system self-organizes into a ferromagnetic Quantum Anomalous Hall state in which the direction of its dissipationless edge-currents can be switched by an applied magnetic field. PACS numbers: 71.27.+a , Introduction.-The study of topologically non-trivial states of matter is one of the hottest topics in present day condensed matter physics. An understanding of topological states requires a theoretical paradigm that goes far beyond the concept of global symmetry breaking that has originally been laid out by Landau. It is remarkable that the theoretical predictions on the existence of various topologically ordered states have rather swiftly led to the discovery of an entirely new class of materials, the topological insulators [1][2][3][4]. Recent pioneering experiments have confirmed the key signatures of nontrivial topology in certain materials, e.g. spin-momentumlocked undoubled Dirac fermions [5][6][7] and the Quantum Spin Hall (QSH) effect [8]. These topological insulators are timereversal (TR) invariant generalizations of the first, much older, topological state of matter, the famous Integer Quantum Hall states [9,10] that are induced by a magnetic field, which obviously breaks TR symmetry.In a seminal work in 1988, Haldane established that a magnetic field is not required to induce states with the same topology as IQH states [11]. It was shown that adding complex hopping to a graphene-like Hamiltonian for electrons on a honeycomb lattice opens up topologically nontrivial gaps at the Dirac points, which yields a topologically ordered, insulating state, referred to as a Quantum Anomalous Hall (QAH) state. An important feature of QAH states are edge channels, in which current can run only in one direction; in contrast to QSH states, on a single edge the opposite spin channel carrying the opposite current is absent [12]. QAH states would thus allow very robust, dissipationless charge transport along edge channels, as backscattering would be completely suppressed. However, while signatures of QAH behavior have been reported in some compounds [13][14][15], the QAH state is the only one among these topologically insulating states that remains to be unambiguously identified in experiment.The experimental difficulty is mirrored by the frailty of theoretical mass-generating mechanisms for a graphene-like kinetic energy with a linear dispersion at the Fermi level. TRsymmetry breaking via (magnetic) order requires rather specific and strong longer-range Coulomb interactions [16], because the Dirac cones' vanishing density of states at the Fermi level r...