An effective low-energy Hamiltonian of itinerant electrons for iridium oxide Na2IrO3 is derived by an ab initio downfolding scheme. The model is then reduced to an effective spin model on a honeycomb lattice by the strong coupling expansion. Here we show that the ab initio model contains spin-spin anisotropic exchange terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, and allows to describe the experimentally observed zigzag magnetic order, interpreted as the state stabilized by the antiferromagnetic coupling of the ferromagnetic chains. We clarify possible routes to realize quantum spin liquids from existing Na2IrO3.Introduction.-Cooperation and competition between strong electron correlations and spin-orbit couplings have recently attracted much attention. Iridium oxides offer playgrounds for such an interplay and indeed exhibit intriguing rich phenomena [1][2][3][4].

We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combination allows an application of the machine learning scheme to interacting fermionic systems. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.

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Contrary to the original expectation, Na2IrO3 is not a Kitaev's quantum spin liquid (QSL) but shows a zig-zag-type antiferromagnetic order in experiments. Here we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka et al. in Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na2IrO3 proposed by Yamaji et al. in Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Néel temperatures: (1) Two peaks in the temperature dependence of specific heat at T ℓ and T h caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, prominent plateau or shoulder pinned at R 2 ln 2 in the temperature dependence of entropy, where R is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio T ℓ /T h close to or less than 0.03. According to the proposed criteria, Na2IrO3 is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na2IrO3 on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na1−xLix)2IrO3 and other related materials are also discussed.

We study roles of electron correlations on topological insulators on the honeycomb lattice with the spin-orbit interaction. Accurate variational Monte Carlo calculations show that the increasing onsite Coulomb interactions cause a strong suppression of the charge Drude weight in the helical-edge metallic states leading to a presumable Mott transition from a conventional topological insulator to an edge Mott insulator before a transition to a bulk antiferromagnetic insulator. The intermediate bulk-topological and edge-Mott-insulator phase has a helical spin-liquid character with the protected time-reversal symmetry.-Introduction. Recently, spin Hall insulators and its generalization, topological insulators (TIs) have attracted much attention as a new state of matter [1]. A remarkable feature of the newly discovered quantum phase is the Z 2 -type topological distinction from other conventional phases as well as the existence of robust gapless edges or surface states concomitant with the bulk insulating gap, which are all protected by the time reversal (TR) symmetry. The edge or surface modes of TI provide us with truly one-or two-dimensional gapless and metallic electronic states.It has also been proposed that TI may appear in systems under substantial electron correlations such as in 4d or 5d transition metal oxides [2][3][4][5][6], while the interplay of electron correlations with the topological insulator has not been well understood, although the absence of the back scattering protected by the time reversal symmetry is expected to suppress electron correlation effects [1,7,8].In this Letter, based on results of calculations obtained from a multi-variable variational Monte Carlo (MVMC) methods improved by Tahara and one of the authors[9], we propose that electron correlation effects introduced by an onsite interaction, namely, a Hubbard U in the Kane-Mele model on the honeycomb lattice allow a transition from the above TI to an unconventional TI phase characterized by the charge gapful (insulating) but spin gapless edge excitations with a nonzero spin Drude weight within the same preserved topological nontriviality of the bulk states that are protected by the time reversal symmetry. This new topological edge Mott insulator (TEMI) phase is stabilized in a region of the intermediate correlation strength sandwiched by a bulk antiferromagnetic insulator (BAFI) with the broken time reversal symmetry (or bulk Mott insulator (BMI)) in the larger U region and the simple TI insulator in the weak correlation region.-Model. We study a tight binding hamiltonian on the two-dimensional honeycomb lattice proposed by Kane and Mele [1] with inclusion of the on-site Coulomb interaction, and without the Rashba term to study electron correlation effects on the topological insulator. Hereafter we call this simple model the Hubbard-Kane-Mele model and is defined aŝwitĥ (2) whereĤ KM is the Kane-Mele hamiltonian and U generates an onsite Hubbard interaction between the up and down spin electrons. Here we define ν ij = d i × d j / d i ...