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Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first-(J1) and second-neighbor (J2) interactions (0.0≤J2/J1≤0.5) by means of density-matrix renormalization group. In the parameter regime J2/J1≲0.27, the system sustains a Néel antiferromagnetic phase. At the large J2 side J2/J1≳0.32, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases 0.27≲J2/J1≲0.32, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/2 system. [ABSTRACT FROM AUTHOR]

The two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model on a honeycomb lattice has been shown to be a universal resource for quantum computation. In this valence bond solid, however, the spin interactions involve higher powers of the Heisenberg coupling (Si - Sj)n, making these states seemingly unrealistic on bipartite lattices, where one expects a simple antiferromagnetic order. We show that those interactions can be generated by orbital physics in multiorbital Mott insulators. We focus on t2g electrons on the honeycomb lattice and propose a physical realization of the spin-3/2 AKLT state. We find a phase transition from the AKLT to the Neel state on increasing Hund's rule coupling, which is confirmed by density matrix renormalization group simulations. An experimental signature of the AKLT state consists of protected, free 5 = 1/2 spins on lattice vacancies, which may be detected in the spin susceptibility. [ABSTRACT FROM AUTHOR]

We use numerical linked cluster expansions to study the thermodynamic properties of the two-dimensional classical Ising, quantum XY, and quantum Heisenberg models with bimodal random-bond disorder on the square and honeycomb lattice. In all cases, the nearest-neighbor coupling between the spins takes values ± J with equal probability. We obtain the disorder-averaged (over ah disorder configurations) energy, entropy, specific heat, and uniform magnetic susceptibility in each case. These results are compared with the corresponding ones in the clean models. Analytic expressions are obtained for low orders in the expansion of these thermodynamic quantities in inverse temperature. [ABSTRACT FROM AUTHOR]

We exploit a natural projected entangled-pair state (PEPS) representation for the resonating Affleck-Kennedy- Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On the kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a Z2 spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range resonating valence bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS. [ABSTRACT FROM AUTHOR]

We examine the stability of classical states with a generic incommensurate spiral order against quantum fluctuations. Specifically, we focus on the frustrated spin-1/2 XY and Heisenberg models on the honeycomb lattice with nearest-neighbor J1 and next-nearest-neighbor J2 antiferromagnetic couplings. Our variational approach is based on the Jastrow wave functions, which include quantum correlations on top of classical spin waves. We perform a systematic optimization of wave vectors and Jastrow pseudopotentials within this class of variational states and find that quantum fluctuations favor collinear states over generic coplanar spirals. The Néel state with Q = (0,0) extends its stability well beyond the classical value J2/J1 = 1/6. Most importantly, the collinear states with Q = (0,2π/√3) (and the two symmetry-related states) are found to be stable in a large regime with intermediate frustration, while at the classical level they are limited to the point J2/J1 = 0.5. For large frustration, the 120° state is stabilized for finite values of J2/J1 in both models. [ABSTRACT FROM AUTHOR]

We study the finite-temperature phase diagram of the Heisenberg-Kitaev model on a three-dimensional hyperhoneycomb lattice. Using semiclassical analysis and classical Monte Carlo simulations, we investigate quantum and thermal order-by-disorder, as well as the magnetic-ordering temperature. We find the parameter regime where quantum and thermal fluctuations favor different magnetic orders, which leads to an additional finite-temperature phase transition within the ordered phase. This transition, however, occurs at a relatively low temperature and the entropic effects may dominate most of the finite-temperature region below the ordering temperature. In addition, we explore the magnetization process in the presence of a magnetic field and discover spin-flop transitions which are sensitive to the applied-field direction. We discuss implications of our results for future experiments on a hyperhoneycomb lattice system such as the recently discovered β-Li2IrO3. [ABSTRACT FROM AUTHOR]

We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-½ Heisenberg model on a honeycomb lattice with first (J1) and second (J2) neighbor antiferromagnetic interactions, where a Z2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size N = 2 × 6 × 6. With increasing J2, we find a Néel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment ms² on finite-size cylinders to the thermodynamic limit, we find the Néel order vanishing at J2/J1 ≃ 0.22. For 0.25 < J2/J1 ⩽ 0.35, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For 0.22 < J2 < 0.25, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region. [ABSTRACT FROM AUTHOR]

Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al., Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory suggested a dimerized, color-ordered state (Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension D. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small D the dimer state has a lower variational energy than the plaquette state; however, for large D it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are nonchiral flux states. [ABSTRACT FROM AUTHOR]

Using the density matrix renormalization group, we determine the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with a nearest-neighbor interaction J1 and a frustrating, next-nearest-neighbor exchange J2. As frustration increases, the ground state exhibits Néel, plaquette, and dimer orders, with critical points at J2/J1=0.22 and 0.35. We observe that both the spin gap and the corresponding order parameters vanish continuously at both the critical points, indicating the presence of deconfined quantum criticality. [ABSTRACT FROM AUTHOR]

We study the magnetic phase diagram of the J1-J2 Heisenberg antiferromagnet on a honeycomb lattice at the strongly frustrated point J2/J1=1/2 using large-scale Monte Carlo simulations. At low temperatures we find three different field regimes, each characterized by different broken discrete symmetries. In low magnetic fields up to hc1/J1≈2.9 the Z3 rotational lattice symmetry is spontaneously broken while a 1/2-magnetization plateau is stabilized around hc2/J1=4. The collinear plateau state and the coplanar state in higher fields break the Z4 translational symmetry and correspond to triple-q magnetic structures. The intermediate phase hc1

We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, J and ̃J, where J is for the conventional spin and ̃ is for rotated spin. When J = 0, the system is either in a stripy antiferromagnetic order (̃ < 0, ferromagnetic for rotated spin) or a zigzag antiferromagnetic order (̃ > 0, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or between two antiferromagnetic orders induces Kitaev's spin liquid phase, characterized by the exactly solvable Kitaev model (J = ̃). Our model can be applied to layered Mott insulators A2IrO3 (A = Li, Na). For a monolayer of Li2IrO3, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling. [ABSTRACT FROM AUTHOR]

We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N = 3) and the checkerboard lattice (for N = 4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a twofold degeneracy, in which the N spins belonging to a simplex (i.e., a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models. [ABSTRACT FROM AUTHOR]

The competition between Kitaev and Heisenberg interactions away from half filling is studied for the hole-doped Kitaev-Heisenberg t-JK-JH model on a honeycomb lattice. While the isotropic Heisenberg coupling supports a time-reversal violating d-wave singlet state, we find that the Kitaev interaction favors a time-reversal invariant p-wave superconducting phase, which obeys the rotational symmetries of the microscopic model, and is robust for JH < JK/2. Within the p-wave superconducting phase, a critical chemical potential |μ| = μc &ap; t separates a topologically trivial phase for |μ| < μc from a topologically nontrivial Z2 time-reversal invariant spin-triplet phase for |μ| > μc. [ABSTRACT FROM AUTHOR]

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition. [ABSTRACT FROM AUTHOR]

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2Ir03 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from &thetas; = --125 K for Na2Ir03 to &thetas; &thkap; --33 K for Li2Ir03, while the ordering temperature remains roughly the same TN &thkap; 15 K. Using functional renormalization group calculations we show that this evolution of &thetas; and TN as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2Ir03 is deep in a magnetically ordered regime, while Li2Ir03 appears to be close to a spin-liquid regime. [ABSTRACT FROM AUTHOR]

Motivated by the observation of a disordered spin ground state in the S = 3/2 material Bi3Mn4O12NO3, we study the ground-state properties and excitation spectra of the S = 3/2 (and for comparison S = 1/2) bilayer Heisenberg model on the honeycomb lattice, with and without frustrating further neighbor interactions. We use series expansions around the Néel state to calculate properties of the magnetically ordered phase. Furthermore, series expansions in 1/&lgr; = J1/J⊥, where J⊥ is an in-plane exchange constant and Jx is the exchange constant between the layers, are used to study properties of the spin singlet phase. For the unfrustrated case, our results for the phase transitions are in very good agreement with recent quantum Monte Carlo studies. We also obtain the excitation spectra in the disordered phase and study the change in the critical &lgr; when frustrating exchange interactions are added to the S = 3/2 system and find a rapid suppression of the ordered phase with frustration. Implications for the material Bi3Mn4O12NO3 are discussed. [ABSTRACT FROM AUTHOR]

A Kitaev-Heisenberg- J2-J3 model is proposed to describe the Mort-insulating layered iridates A2IrO3 (A = Na, Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest-neighbor couplings J1, J2, and J3. A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the J1-J2-J3 one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings. [ABSTRACT FROM AUTHOR]

We develop high-temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity, and entropy as a function of temperature for different values of the Kitaev coupling K and Heisenberg exchange coupling J (with |J|≤|K|) are presented. These expansions show good convergence down to a temperature of a fraction of K and in some cases down to T=K/10. In the Kitaev exchange dominated regime, the inverse susceptibility has a nearly linear temperature dependence over a wide temperature range. However, we show that already at temperatures ten times the Curie-Weiss temperature, the effective Curie-Weiss constant estimated from the data can be off by a factor of 2. We find that the magnitude of the heat-capacity maximum at the short-range-order peak, is substantially smaller for small J/K than for J of order or larger than K. We suggest that this itself represents a simple marker for the relative importance of the Kitaev terms in these systems. Somewhat surprisingly, both heat-capacity and susceptibility data on Na2IrO3 are consistent with a dominant antiferromagnetic Kitaev exchange constant of about 300-400K. [ABSTRACT FROM AUTHOR]

Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor J1 and second-neighbor J2 antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio J2/J1, we find strong evidence for a continuous transition to a nonmagnetic phase at J2/J1≈0.23. Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For 0.23≲J2/J1≲0.36, a gapless Z2 spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the Néel order melts, this ordered state becomes clearly favored only for J2/J1≳0.3. Finally, for 0.36≲J2/J1≤0.5, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the Néel antiferromagnet from the plaquette valence-bond solid. [ABSTRACT FROM AUTHOR]