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We study the two-dimensional Kane-Mele-Hubbard model at half filling by means of quantum Monte Carlo simulations. We present a refined phase boundary for the quantum spin liquid. The topological insulator at finite Hubbard interaction strength is adiabatically connected to the groundstate of the Kane-Mele model. In the presence of spin-orbit coupling, magnetic order at large Hubbard U is restricted to the transverse direction. The transition from the topological band insulator to the antiferromagnetic Mott insulator is in the universality class of the three-dimensional XY model. The numerical data suggest that the spin liquid to topological insulator and spin liquid to Mott insulator transitions are both continuous.Comment: 13 pages, 10 figures; final version; new Figs. 4(b) and 8(b

Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.

We consider the Kane-Mele model supplemented by a Hubbard U term. The phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. The quantum spin liquid of the Hubbard model is robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U > Uc both states are unstable toward magnetic ordering. In the quantum spin-Hall state we study the spin, charge and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on a ribbon edge. The Hubbard interaction greatly suppresses charge currents along the edge and promotes edge magnetism, but leaves the single-particle signatures of the helical liquid intact.

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the π-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.

The superfluid to Mott insulator transition in cavity polariton arrays is analyzed using the variational cluster approach, taking into account quantum fluctuations exactly on finite length scales. Phase diagrams in one and two dimensions exhibit important non-mean-field features. Single-particle excitation spectra in the Mott phase are dominated by particle and hole bands separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows for changing the nature of the bosonic particles from quasilocalized excitons to polaritons to weakly interacting photons. The Mott state with density one exists up to temperatures T /g 0.03, implying experimentally accessible temperatures for realistic cavity couplings g. PACS numbers: 71.36.+c, 73.43.Nq, 78.20.Bh, 42.50.Ct The prospect of realizing a tunable, strongly correlated system of photons is exciting, both as a testbed for quantum many-body dynamics and for the potential of quantum simulators and other advanced quantum devices. Three proposals based on cavity-QED arrays have recently shown how this might be accomplished [1,2,3], followed by further work [4,5,6,7,8]. Engineered strong photon-photon interactions and hopping between cavities allow photons (as a component of cavity polaritons) to behave much like electrons or atoms in a many-body context. It is clear that a particular signature of quantum many-body physics, the superfluid (SF) to Mott insulator (MI) transition, should be reproducible in such systems and be similar to the widely studied Bose-Hubbard model (BHM). Yet, the BH analogy is not complete. The mixed matter-light nature of the system brings new physics yet to be fully explored."Solid-light" systems-so-named for the intriguing MI state of photons they exhibit-are reminiscent of cold atom optical lattices (CAOL) [9], but have some advantages concerning direct addressing of individual sites and device integration, and the potential for asymmetry construction by individual tuning, local variation, and far from equilibrium devices [4]. Photons as part of the system serve as excellent experimental probes, and have excellent "flying" potential so that they can be transported over long distances. Temporal and spatial correlation functions are accessible, and nonequilibrium quantum dynamics may be studied using coherent laser pumping to create initial states. Here ω 0 is the cavity photon energy, and ∆ = ω 0 − ǫ defines the detuning. Each cavity is described by the well-known Jaynes-Cummings (JC) HamiltonianĤ JC . The atom-photon coupling g (a † i , a i are photon creation and annihilation operators) gives rise to formation of polaritons (combined atomphoton excitations) whose numberN p = i (a † i a i +|↑ i ↑ i |) is conserved and couples to the chemical potential µ [7]. We consider nearest-neighbor photon hopping with amplitude t, define the polariton density n = N p /L, use g as the unit of energy and set ω 0 /g [23], k B and the lattice constant to one.Hamiltonian (1) represents a generic model of strongly correlated photons amenable to numer...

We use exact diagonalization and cluster perturbation theory to address the role of strong interactions and quantum fluctuations for spinless fermions on the honeycomb lattice. We find quantum fluctuations to be very pronounced both at weak and strong interactions. A weak second-neighbor Coulomb repulsion $V_2$ induces a tendency toward an interaction-generated quantum anomalous Hall phase, as borne out in mean-field theory. However, quantum fluctuations prevent the formation of a stable quantum Hall phase before the onset of the charge-modulated phase predicted at large $V_2$ by mean-field theory. Consequently, the system undergoes a direct transition from the semimetal to the charge-modulated phase. For the latter, charge fluctuations also play a key role. While the phase, which is related to pinball liquids, is stabilized by the repulsion $V_2$, the energy of its low-lying charge excitations scales with the electronic hopping $t$, as in a band insulator.Comment: 9 pages, 7 figures; final versio