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Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer of an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction, J, is analyzed through Abrikosov fermion mean-field theory. The system sustains quantum spin liquid (QSL) solutions which have different character depending on parity of the number of layers. While in even layered Kitaev models a gapped QSL emerges, odd-layered models host gapless QSLs. The projective symmetry group analysis of these solutions unravel a layer-to-layer inversion symmetry rather than an expected reflection. Although these QSLs retain features of the single layer Kitaev spin liquid (KSL), they should be regarded hybrid QSLs consisting on several KSLs. The good agreement at large-J between the energy of the Gutzwiller projected mean-field QSL and the exact energy indicates that such QSL Ansatz is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of alpha-RuCl3 and H3LiIr2O6 which are examples of magnetically coupled multilayer Kitaev models., Comment: 16 pages, 8 figures

Motivated by the possibility of finding a bosonic quantum spin liquid in the integer spin-$S$ Heisenberg-Kitaev model on the honeycomb lattice, we derive a Schwinger boson mean field theory involving both singlet and triplet pairing channels which includes hopping and pairing operators on equal footing. The mixed construction introduced here is justified by the good comparison with exact diagonalization energies of the $S \leq 3/2$ Heisenberg-Kitaev model and the perfect match with the Luttinger-Tisza semiclassical energies obtained at large-$S$. We find various competing gapped quantum spin liquids close to the Kitaev point. A comparison of their spin excitation spectrum with the dynamical structure factor obtained from exact diagonalizations allows us to identify the physical spin liquid $ans\"atz$ of the model. In particular, we identify a chiral quantum spin liquid state whose spin excitation spectrum follows closely the exact diagonalization data and survives up to large spin $S \lesssim 2$. We propose this state as a promising quantum spin liquid candidate for the integer spin-$S$ antiferromagnetic Kitaev model which may be realized in $S=1$ Kitaev materials A$_3$Ni$_2$XO$_6$ and KNiAsO$_4$., Comment: 13 pages, 11 figures

$\require{mhchem}$The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized $\ce{Na6Cu7BiO4(PO4)4Cl3}$ where a Cu$^{2+}$ spin-$1/2$ square-kagome lattice (with six site unit cell) is decorated by a seventh magnetic site alternatingly above and below the layers. The material does not show any sign of long-range magnetic order down to 50 mK despite a Curie-Weiss temperature of $-212$ K indicating a quantum paramagnetic phase. Our DFT energy mapping elicits a purely antiferromagnetic Hamiltonian that features longer range exchange interactions beyond the pure square-kagome model and, importantly, we find the seventh site to be strongly coupled to the plane. We combine two variational Monte Carlo approaches, pseudo-fermion/Majorana functional renormalization group and Schwinger-Boson mean field calculations to show that the complex Hamiltonian of $\ce{Na6Cu7BiO4(PO4)4Cl3}$ still features a nonmagnetic ground state. We explain how the seventh Cu$^{2+}$ site actually aids the stabilization of the disordered state. We predict static and dynamic spin structure factors to guide future neutron scattering experiments., Comment: 5 pages, 4 figures. Supplement: 7 pages, 11 figures v2: minor revisions in text and figure labels

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus., Comment: Last version before publication in PRB

The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid with Majorana excitations, Chern number +/-4 and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral quantum spin liquid, an orbital effect of an applied magnetic field and spin orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. We interpret the large thermal Hall effect observed in Mott cuprates from their close proximity to a transition to a Majorana chiral quantum spin liquid which can be induced by an external magnetic field., Comment: 6 pages, 4 figures + supplemental material

A spin-1/2 Heisenberg model on honeycomb lattice is investigated by doing triplon analysis and quantum Monte Carlo calculations. This model, inspired by Cu$_2$(pymca)$_3$(ClO$_4$), has three different antiferromagnetic exchange interactions ($J_A$, $J_B$, $J_C$) on three different sets of nearest-neighbour bonds which form a kagome superlattice. While the model is bipartite and unfrustrated, its quantum phase diagram is found to be dominated by a quantum paramagnetic phase that is best described as a spin-gapped hexagonal-singlet state. The N\'eel antiferromagnetic order survives only in a small region around $J_A=J_B=J_C$. The magnetization produced by external magnetic field is found to exhibit plateaus at 1/3 and 2/3 of the saturation value, or at 1/3 alone, or no plateaus. Notably, the plateaus exist only inside a bounded region within the hexagonal-singlet phase. This study provides a clear understanding of the spin-gapped behaviour and magnetization plateaus observed in Cu$_2$(pymca)$_3$(ClO$_4$), and also predicts the possible disappearance of 2/3 plateau under pressure., Comment: 16 pages, 14 figures

In correlated electron systems the metallic character of a material can be strongly suppressed near an integer concentration of conduction electrons as Coulomb interactions forbid the double occupancy of local atomic orbitals. While the Mott-Hubbard physics arising from such on-site interactions has been largely studied, several unexplained phenomena observed in correlated materials challenge this description and call for the development of new ideas. Here we explore a general route for obtaining correlated behavior that is decidedly different from the spin-related Mott-Hubbard mechanism and instead relies on the presence of unscreened, long-range Coulomb interactions. We find a pseudogap metal phase characterized by a divergent quasiparticle mass and the opening of a Coulomb pseudogap in the electronic spectrum. The destruction of the Fermi-liquid state occurs because the electrons move in a nearly frozen, disordered charge background, as collective charge rearrangements are drastically slowed down by the frustrating nature of long-range potentials on discrete lattices. The present pseudogap metal realizes an early conjecture by Efros, that a soft Coulomb gap should appear for quantum lattice electrons with strong unscreened interactions due to self-generated randomness., Comment: 4 pages + 4 pages supplementary information

We present a mechanical analog of a quantum wave-particle duality: a vibrating string threaded through a freely moving bead or `masslet'. For small string amplitudes, the particle movement is governed by a set of non-linear dynamical equations that couple the wave field to the masslet dynamics. Under specific conditions, the particle achieves a regime of {\it transparency} in which the field and the particle's dynamics appear decoupled. In that special case, the particle conserves its momentum and a guiding wave obeying a Klein-Gordon equation, with real or imaginary mass, emerges. Similar to the double-solution theory of de Broglie, this guiding wave is locked in phase with a modulating group-wave co-moving with the particle. Interestingly, both subsonic and supersonic particles can fall into a quantum regime as with the slower-than-light bradyons and hypothetical, faster-than-light tachyons of particle physics., Comment: 10 pages, 3 figures, 1 video (Supp. Mat)

Mott insulators under sufficiently strong spin-orbit coupling can display quantum spin liquid phases with topological order and fractional excitations. Quantum magnets with pure Kitaev spin exchange interactions can host a gapped quantum spin liquid with a single Majorana edge mode propagating in the counter-clockwise direction when a small positive magnetic field is applied. Here, we show how under a sufficiently strong positive magnetic field a topological transition into a gapped quantum spin liquid with two Majorana edge modes propagating in the clockwise direction occurs. The Dzyaloshinskii-Moriya interaction is found to turn the non-chiral Kitaev's gapless quantum spin liquid into a chiral one with equal Berry phases at the two Dirac points. Thermal Hall conductance experiments can provide evidence of the novel topologically gapped quantum spin liquid states predicted., Comment: last version, 4 pages, 4 figures + Supplemental material

The ground state of the spin$-1/2$ kagome antiferromagnet remains uncertain despite decades of active research. Here we step aside from this debated question to address the ground-state nature of a related, and potentially just as rich, system made of corner-sharing triangles: the square-kagome lattice (SKL). Our work is motivated by the recent synthesis of a distorted SKL compound mentioned in [Morita & Tohyama, J. Phys. Soc. Japan 87, 043704 (2018)]. We have studied its spin$-1/2$ $J_{1}$-$J_{2}$ phase diagram with an unrestricted Schwinger boson mean-field theory (SBMFT). We show that, in addition of agreeing with previous studies, three original phases appear: two incommensurate orders and a topological quantum spin liquid with weak nematicity. The topological order is characterized by fluxes on specific gauge-invariant quantities and the phase is stable under anisotropic perturbations relevant for experiments. Finally, we provide dynamical structure factors of the reported phases that could be observed in inelastic neutron scattering., Comment: Core text updated, 2 appendices added with 4 new figures

The spin-1/2 Heisenberg model on the kagome lattice, which is closely realized in layered Mott insulators such as ZnCu$_3$(OH)$_6$Cl$_2$, is one of the oldest and most enigmatic spin-1/2 lattice model. While the numerical evidence has accumulated in favor of a quantum spin liquid, the debate is still open as to whether it is a $Z_2$ spin liquid with very short-range correlations (some kind of Resonating Valence Bond spin liquid), or an algebraic spin-liquid with power-law correlations. To address this issue, we have pushed the program started by Rokhsar and Kivelson in their derivation of the effective quantum dimer model description of Heisenberg models to unprecedented accuracy for the spin-1/2 kagome, by including all the most important virtual singlet contributions on top of the orthogonalization of the nearest-neighbor valence bond singlet basis. Quite remarkably, the resulting picture is a competition between a $Z_2$ spin liquid and a diamond valence bond crystal with a 12-site unit cell, as in the DMRG simulations of Yan, Huse and White. Furthermore, we found that, on cylinders of finite diameter $d$, there is a transition between the $Z_2$ spin liquid at small $d$ and the diamond valence bond crystal at large $d$, the prediction of the present microscopic description for the 2D lattice. These results show that, if the ground state of the spin-1/2 kagome antiferromagnet can be described by nearest-neighbor singlet dimers, it is a diamond valence bond crystal, and, a contrario, that, if the system is a quantum spin liquid, it has to involve long-range singlets, consistent with the algebraic spin liquid scenario., Comment: 11 pages, 14 figures. Revised and extended version. Results are untouched, implications have been clarified and better put in context

In the absence of disorder, electrons can display glassy behavior through supercooling the liquid state, avoiding the solidification into a charge ordered state. Such supercooled electron liquids are experimentally found in organic $\theta$-$MM'$ compounds. We present theoretical results that qualitatively capture the experimental findings. At intermediate temperatures, the conducting state crosses over into a weakly insulating pseudogap phase. The stripe order phase transition is first order, so that the liquid phase is metastable below $T_s$. In the supercooled liquid phase the resistivity increases further and the density of states at the Fermi level is suppressed, indicating kinetic arrest and the formation of a glassy state. Our results are obtained using classical Extended Dynamical Mean Field Theory., Comment: 4 pages, 4 figures, submitted to the proceedings of "Superstripes 2015", Journal of Superconductivity and Novel Magnetism (2015)

It is well known that in quantum spin liquids and other magnetically disordered systems, the tunneling amplitudes between different nearest-neighbor valence bond (NNVB) configurations drop exponentially in the length L of the tunneling loops. Here we show that virtual excursions outside the NNVB basis can alter completely this fundamental quantum-mechanical notion even in extreme cases where the minimal NNVB truncation appears very robust. This paradigm shift is demonstrated for the quantum spin-1/2 square-kagome, where strong geometric frustration, similar to the two-dimensional kagome, prevents magnetic ordering down to zero temperature. The shortest tunneling events suffer from the strongest fluctuations, leading to amplitudes that do not drop exponentially with L, and to an unexpected loop-six valence bond crystal phase, which would otherwise be very far in the parameter space in the absence of virtual singlets. The low-energy effective description gives in addition a clear example of correlated loop processes that depend not only on the type of the loop but also on its lattice embedding, a direct manifestation of the long-range nature of the virtual singlets., Comment: 5 pages, 4 figures + supplementing material

The interplay of non-local Coulomb repulsion and Hund's coupling in the d-orbital manifold in frustrated triangular lattices is analyzed by a mutliband extended Hubbard model. We find a rich phase diagram with several competing phases, including a robust pinball liquid phase, which is an unconventional metal characterized by threefold charge order, bad metallic behavior and the emergence of high spin local moments. Our results naturally explain the anomalous charge-ordered metallic state observed in the triangular layered compound AgNiO2. The potential relevance to other triangular transition metal oxides is discussed., Comment: 4 pages, 4 figures

We show that introducing long-range Coulomb interactions immediately lifts the massive ground state degeneracy induced by geometric frustration for electrons on quarter-filled triangular lattices in the classical limit. Important consequences include the stabilization of a stripe-ordered crystalline (global) ground state, but also the emergence of very many low-lying metastable states with amorphous "stripe-glass" spatial structures. Melting of the stripe order thus leads to a frustrated Coulomb liquid at intermediate temperatures, showing remarkably slow (viscous) dynamics, with very long relaxation times growing in Arrhenius fashion upon cooling, as typical of strong glass formers. On shorter time scales, the system falls out of equilibrium and displays the aging phenomena characteristic of supercooled liquids above the glass transition. Our results show remarkable similarity with the recent observations of charge-glass behavior in ultra-clean triangular organic materials of the $\theta$-(BEDT-TTF)$_2$ family., Comment: 5 pages,4 figures

We investigate the organized formation of strain, ripples and suspended features in macroscopic CVD-prepared graphene sheets transferred onto a corrugated substrate made of an ordered arrays of silica pillars of variable geometries. Depending on the aspect ratio and sharpness of the corrugated array, graphene can conformally coat the surface, partially collapse, or lay, fakir-like, fully suspended between pillars over tens of micrometers. Upon increase of pillar density, ripples in collapsed films display a transition from random oriented pleats emerging from pillars to ripples linking nearest neighboring pillars organized in domains of given orientation. Spatially-resolved Raman spectroscopy, atomic force microscopy and electronic microscopy reveal uniaxial strain domains in the transferred graphene, which are induced and controlled by the geometry. We propose a simple theoretical model to explain the transition between suspended and collapsed graphene. For the arrays with high aspect ratio pillars, graphene membranes stays suspended over macroscopic distances with minimal interaction with pillars tip apex. It offers a platform to tailor stress in graphene layers and open perspectives for electron transport and nanomechanical applications.

We study the phase diagram of the extended Hubbard model on the kagome lattice at 1/3 filling. By combining a configuration interaction approach to an unrestricted Hartree-Fock, we construct an effective hamiltonian which takes the correlations back on top of the mean-field solution. We obtain a rich phase diagram with, in particular, the presence of two original phases. The first one consists of polarized droplets of metal standing on the hexagons of the lattice, and an enlarged kagome charge order, inversely polarized, on the remaining sites. The second, obeying a local ice-rule type constraint on the triangles of the kagome lattice, is driven by an antiferromagnetically coupling of spins and is constituted of disconnected 6-spin singlet rings. The nature and stability of these phases at large interactions is studied via variational wave functions and perturbation theory., Comment: 6 pages, 5 figures

We study charge ordering driven by Coulomb interactions on triangular lattices relevant to the Wigner-Mott transition in two dimensions. Dynamical mean-field theory reveals the pinball liquid phase, a charge ordered metallic phase containing quasi-localized (pins) coexisting with itinerant (balls) electrons. Based on an effective periodic Anderson model for this phase, we find an antiferromagnetic Kondo coupling between pins and balls and strong quasiparticle renormalization. Non-Fermi liquid behavior can occur in such charge ordered systems due to spin-flip scattering of itinerant electrons off the pins in analogy with heavy fermion compounds., Comment: 5 pages, 3 figures

Band ferromagnetism in strongly correlated electron systems is one of the most challenging issue in today's condensed-matter physics. In this theoretical work, we study the competition between kinetic term, Coulomb repulsion, and on-site correlated disorder for various lattice geometries. Unconventional and complex ferromagnetic phase diagrams are obtained: wide region of stability, cascade of transitions, re-entrance, high sensitivity to the carrier concentration and strongly inhomogeneous ground states for relatively weak on-site potential. The direct and systematic comparison with Exact Diagonalization shows that the Unrestricted Hartree-Fock method is unexpectedly accurate for such systems, which allows large size cluster calculations. A match of the order of 99.9% for weak and intermediate couplings is found, slightly reduced to about 95% in the large repulsion regime. Nano-patterned lattices appear to be particularly promising candidates that could, with the tremendous progress in growing and self-organized techniques, be synthesized in a near future., Comment: 6 pages, 8 figures

We study a model for orbitally degenerate Mott insulators, where localized electrons possess t_2g degrees of freedom coupled by several, competing, exchange mechanisms. We provide evidence for two distinct strongly fluctuating regimes, depending on whether superexchange or direct exchange mechanism predominates. In the superexchange-dominated regime, the ground state is dimerized, with nearest neighbor orbital singlets covering the lattice. By deriving an effective quantum dimer model and analyzing it numerically, we characterize this dimerized phase as a valence bond crystal stabilized by singlet resonances within a large unit cell. In the opposite regime, with predominant direct exchange, the combined analysis of the original model and another effective model adapted to the local constraints, shows that subleading perturbations select a highly resonating ground state, with coexisting diagonal and off-diagonal long-range orbital orders., Comment: 14 pages, 13 figures

The phase diagram of the XXZ spin-1/2 magnet, equivalent to hard-core bosons, under a staggered magnetic field and on the Cairo pentagonal lattice is computed at zero and finite temperature by using a cluster mean field theory and a stochastic series expansion quantum Monte Carlo.The complex connectivity and the frustration lead to unconventional phases such as a 1/3-ferrimagnetic plateau stabilized by quantum fluctuations as well as a 5/12-topological phase induced by a local ice-rule constraint. We also report the presence of a ferrimagnetic superfluid and its thermal melting. Finally, we discuss the ferro- and antiferro- magnetic (hopping sign) cases., Comment: 5 pages, 5 figures

We show that the liquid-to-crystal quantum phase transition in the Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortex-like excitations called ``visons''. This conclusion is drawn from the numerical studies of the vison spectrum in the liquid phase by using the Green's function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement with the earlier prediction of Moessner and Sondhi [Phys. Rev. B 63, 224401 (2001)]., Comment: 4 pages, 4 figures

We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell., Comment: 6 pages, 8 figures

Starting from the mean-field solution of a spin-orbital model of LiNiO$_2$, we derive an effective quantum dimer model (QDM) that lives on the triangular lattice and contains kinetic terms acting on 4-site plaquettes and 6-site loops. Using numerical exact diagonalizations and Green's function Monte Carlo simulations, we show that the competition between these kinetic terms leads to a resonating valence bond (RVB) state for a finite range of parameters. We also show that this RVB phase is connected to the RVB phase identified in the Rokhsar-Kivelson model on the same lattice in the context of a generalized model that contains both the 6--site loops and a nearest-neighbor dimer repulsion. These results suggest that the occurrence of an RVB phase is a generic feature of QDM with competing interactions., Comment: 8 pages, 12 figures

A family of models is proposed to describe the motion of holes in a fluctuating quantum dimer background on the square lattice. Following Castelnovo et al. [Ann. Phys. (NY) 318, 316 (2005)], a generalized Rokhsar-Kivelson Hamiltonian at **finite doping** which can be mapped on a **doped** interacting classical dimer model is constructed. A simple physical extension of this model is also considered. Using numerical computations and simple considerations based on the above exact mapping, we determine the phase diagram of the model showing a number of quantum phases typical of a doped Mott insulator. The two-hole correlation function generically exhibits short-range or long-range algebraic correlations in the solid (columnar) and liquid (critical) phases of the model, respectively. Evidence for an extended region of a doped VBS phase exhibiting holon pairing but **no** phase separation is given. In contrast, we show that hole deconfinement occurs in the staggered dimer phase., Comment: 5 pages

Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. {\bf 86}, 1881 (2001)]., Comment: 10 pages, 16 figures