Quantum spin liquids are materials that feature quantum entangled spin correlations and avoid magnetic long-range order at T = 0 K. Particularly interesting are two-dimensional honeycomb spin lattices where a plethora of exotic quantum spin liquids have been predicted. Here, we experimentally study an effective S=1/2 Heisenberg honeycomb lattice with competing nearest and next-nearest neighbor interactions. We demonstrate that YbBr$_3$ avoids order down to at least T=100 mK and features a dynamic spin-spin correlation function with broad continuum scattering typical of quantum spin liquids near a quantum critical point. The continuum in the spin spectrum is consistent with plaquette type fluctuations predicted by theory. Our study is the experimental demonstration that strong quantum fluctuations can exist on the honeycomb lattice even in the absence of Kitaev-type interactions, and opens a new perspective on quantum spin liquids.
We study S=1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J_{1}-J_{2} model), employing exact diagonalization in both S_z=0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2<J_2/J_1<0.3, NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidate for the ground state in the frustrated…
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) sym…
A number of topological nodes including Dirac, quadratic and triple band touching points as well as a pair of degenerate Dirac line nodes are found to emerge in the triplet plaquette excitations of the frustrated spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock spac…
Using the density matrix renormalization group, we investigate the $S=1/2$ Heisenberg model on the honeycomb lattice with first- ($J_1$) and second-neighbor ($J_2$) interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For $J_2/J_1$ near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for $J_2\lesssim 0.26$ and by a valence bond crystal for $J_2\gtrsim 0.36$. The longest correlation length that we find in this intermediate phase is for plaquette valence bond (PVB) order. This correlation length grows strongly with cy…
We study the proposed plaquette-RVB (pRVB) state in the honeycomb lattice $J_1-J_2$ model with frustration arising from next-nearest neighbour interactions. Starting with the limit of decoupled hexagons, we develop a plaquette operator approach to describe the pRVB state and its low energy excitations. Our calculation clarifies that the putative pRVB state necessarily has f-wave symmetry - the plaquette wavefunction is an antisymmetric combination of the Kekulé structures. We estimate the plaquette ordering amplitude, ground state energy and spin gap as a function of $J_2/J_1$. The pRVB state …
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 (LFWT) 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 …
A family of spin-orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal $Γ$ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these systems. However, the ground state of honeycomb $Γ$ model remains elusive, with a suggested zigzag magnetic order. Here we attempt to resolve the puzzle by perturbing the $Γ$ region with a staggered Heisenberg interaction which favours the zigzag orderin…
Motivated by the current interest in the quantum dimer model on the triangular lattice, we investigate the phase diagram of the closely related fully-frustrated transverse field Ising model on the honeycomb lattice using classical and semi-classical approximations. We show that, in addition to the fully polarized phase at large field, the classical model possesses a multitude of phases that break the translational symmetry which in the dimer language, correspond to a plaquette phase and a columnar phase separated by an infinite cascade of mixed phases. The modification of the phase diagram by …
It was known that by a duality transformation, interaction bosons at filling factor $ f=p/q $ hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating{\em dual} " magnetic field" whose average strength through a dual plaquette is equal to the boson density $ f=p/q $.So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of $ f=p/q $ flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux $ f=p/q $ pe…
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-neighbor exchange J2. As frustration increases, the ground state exhibits Neel, 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.
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ 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 $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. C…
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- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 \leq J_2/J_1 \leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 \lesssim 0.27$, the system sustains a Néel antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 \gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phas…
We examine the existence of the interaction-generated quantum anomalous Hall phase on the honeycomb lattice. For the spinless model at half filling, the existence of a quantum anomalous Hall phase (Chern insulator phase) has been predicted using mean-field methods. However, recent exact diagonalization studies for small clusters with periodic boundary condition have not found a clear sign of an interaction-driven Chern insulator phase. We use exact diagonalization method to study properties of small clusters with open boundary condition and, contrary to previous studies, we find clear signatur…
We study the ground-state phase diagram of the quantum $J_1-J_2$ model on the honeycomb lattice by means of an entangled-plaquette variational ansatz. Values of energy and relevant order parameters are computed in the range $0\le {J_2}/{J_1} \le 1$. The system displays classical order for ${J_2}/{J_1}\lesssim 0.2$ (Néel), and for $J_2/J_1 \gtrsim 0.4$ (collinear). In the intermediate region, the ground-state is disordered. Our results show that the reduction of the half-filled Hubbard model to the model studied here does not yield accurate predictions.
Na$_2$IrO$_3$, a honeycomb 5$d^5$ oxide, has been recently identified as a potential realization of the Kitaev spin lattice. The basic feature of this spin model is that for each of the three metal-metal links emerging out of a metal site, the Kitaev interaction connects only spin components perpendicular to the plaquette defined by the magnetic ions and two bridging ligands. The fact that reciprocally orthogonal spin components are coupled along the three different links leads to strong frustration effects and nontrivial physics. While the experiments indicate zigzag antiferromagnetic order i…
We employ the spin cluster perturbation theory to investigate the dynamical properties of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model on the honeycomb lattice. We obtain the excitation spectra for all possible phases in the phase diagram, including the Néel phase, plaquette valence-bond-solid phase, dimer valence-bond-solid phase and stripe antiferromagnetic phase. In the Néel phase, besides the obvious renormalization of the magnon dispersion, we find that the spectrum exhibits a dome-shaped broad continuum around the second Brillouin zone (BZ) and the additional strong continuum c…
We analyze magnetic order in iron-chalcogenide Fe$_{1+y}$Te -- the parent compound of high-temperature superconductor Fe$_{1+y}$Te$_{1-x}$Se$_x$. Neutron scattering experiments show that magnetic order in this material contains components with momentum $Q_1=(π/2, π/2)$ and $Q_2 =(π/2, -π/2)$ in Fe-only Brillouin zone. The actual spin order depends on the interplay between these two components. Previous works argued that spin order is a single-$Q$ state (either $Q_1$ or $Q_2$). Such an order breaks rotational $C_4$ symmetry and order spins into a double diagonal stripe. We show that quantum flu…
We present a comprehensive computational study of the phase diagram of the frustrated S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2) and third-neighbor (J3) couplings. Using a combination of exact diagonalizations of the original spin model, of the Hamiltonian projected into the nearest neighbor short range valence bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region J2,J3\in [0,1], and find a sizable magnetically disorder…
The SU(4) Heisenberg model can serve as a low energy model of the Mott insulating state in materials where the spins and orbitals are highly symmetric, or in systems of alkaline-earth atoms on optical lattice. Recently, it has been argued that on the honeycomb lattice the model exhibits a unique spin-orbital liquid phase with an algebraic decay of correlations [P. Corboz et al., Phys. Rev. X 2, 041013 (2012)]. Here we study the instability of the algebraic spin-orbital liquid toward spontaneous formation of SU(4) singlet plaquettes (tetramerization). Using a variational Monte Carlo approach to…
Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv xJ_{1}>0$. In the range $0<x<1$ we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer, and Néel-II orderings, with quantum critical points at $x_{c_{1}} \approx 0.207(3), x_{c_{2}} \approx 0.385(10)$, and $x_{c_{3}} \approx 0.65(5)$. The transitions at $x_{c_{1}}$ and $x_{c_{3}}$ appear to be continuous (and hence deconfined) ones,…
The phase diagram of the uniaxially anisotropic $s=1$ antiferromagnet on the kagomé lattice includes a critical line exactly described by the classical three-color model. This line is distinct from the standard geometric classical criticality that appears in the classical limit ($s \to \infty$) of the 2D XY model; the $s=1$ geometric T=0 critical line separates two unconventional plaquette-ordered phases that survive to nonzero temperature. The experimentally important correlations at finite temperature and the nature of the transitions into these ordered phases are obtained using the mapping …
We report a new classical spin liquid in which the collective flux degrees of freedom break the translation symmetry of the honeycomb lattice. This exotic phase exists in frustrated spin-orbit magnets where a dominant off-diagonal exchange, the so-called $Γ$ term, results in a macroscopic ground-state degeneracy at the classical level. We demonstrate that the system undergoes a phase transition driven by thermal order-by-disorder at a critical temperature $T_c \approx 0.04 |Γ|$. At first sight, this transition reduces an emergent spherical spin-symmetry to a cubic one: spins point predominantl…
We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a two-dimensional honeycomb lattice numerically by density matrix renormalization group method. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the whole phase diagram with two spin liquid phases and four symmetry broken phases. We identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without Heisenberg interaction. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite di…
We study the effect of quantum fluctuations by means of a transverse magnetic field ($Γ$) on the antiferromagnetic $J_1-J_2$ Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuat…
Flat bands in lattice models have provided useful platforms for studying strong correlation and topological physics. Recently, honeycomb superlattices have been shown to host flat bands that persist in the presence of local perturbations respecting lattice symmetries. We analytically derive the flat band energies in the presence of longer range hopping and find that the energies of flat bands are tunable by these perturbations. In real space, the wave function is constructed from standing waves on each honeycomb edge, allowing the construction of plaquette and loop eigenstates due to destructi…
The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z$_2$ gauge field. Employing an SO(6) Majorana representation of spin 3/2's, we find an exact representation of the conserved plaquette fluxes in terms of static Z$_2$ gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by th…
We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =κJ_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a Néel antiferromagnetic (AFM) phase for $κ< κ_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $κ> κ_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $κ_{c_{1}} \lesssim κ\lesssim κ_{c_{2}}$. …
We establish a way to handle main collective fluctuations in correlated quantum systems based on a Fluctuation Local Field concept. This technique goes beyond standard mean-field approaches, such as Hartree-Fock and dynamical mean-field theories (DMFT), as it includes a fluctuating classical field that acts on the leading order parameter of the system. Effective model parameters of this new theory are determined from the variational principle, which allows to resolve the Fierz ambiguity in decoupling of the local interaction term. In the saddle-point approximation for the fluctuating field our…
We consider the Kane-Mele-Hubbard model with a magnetic $π$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $λ$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase which extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is ex…
We show the chiral d-wave RVB state on honeycomb lattice stands as a natural generalization of the staggered flux phase on square lattice. Although the state is generated from a time reversal symmetry broken mean field ansatz, it actually represents a fully symmetric spin liquid state with a positive definite wave function in the sense of Marshall sign rule for unfrustrated antiferromagnets. The evolution of the state with the parameter $Δ/χ$ follows exactly the same manner as that of the staggered flux phase on square lattice. The critical pairing strength corresponding to the $π$-flux phase …
This article consider a situation of SU(N) system with broken symmetry, and therefore the spin-liquid phase is exist in the phase transition stage. And explore the antiferromagnetic spin interaction with long range order in a two dimension square lattice using the two alkaline earth atoms state short range interaction. The appearance of spin liquid due to noncolline mechanism which causing by destruction of long range order in this model is mentioned. In a N-site fermion-model system, I analyse the effect of fluctuation on order and phase transition. As well as this N-component spin system wit…
We study the exchange physics in high spin Mott insulating systems with $S=3/2$ which is realizable in ultracold atomic systems. The high symmetry of SO(5) or SU(4) therein renders stronger quantum fluctuations than the usual spin-1/2 systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-3/2 model, whose topological excitations exhibit fractionalization behavior. The generalization to the SU(N) plaquette state is also investigated.
In order to understand the properties of Mott insulators with strong ground state orbital fluctuations, we study the zero temperature properties of the SU(4) spin-orbital model on a square lattice. Exact diagonalizations of finite clusters suggest that the ground state is disordered with a singlet-multiplet gap and possibly low-lying SU(4) singlets in the gap. An interpretation in terms of plaquette SU(4) singlets is proposed. The implications for LiNiO_2 are discussed.
Recent experiments on the Co-based $d^7$ honeycomb materials BaCo$_2$(AsO$_4$)$_2$ and BaCo$_2$(PO$_4$)$_2$ have drawn renewed interest to XXZ models with competing interactions beyond the nearest neighbor exchange. While the case of dominant antiferromagnetic exchange has been extensively studied, the actual materials exhibit a ferromagnetic nearest neighbor exchange. Here we show that such a sign change of the dominant nearest neighbor coupling has substantial consequences on the phase diagram. In particular, the nature of the quantum disordered phase of interest changes from a plaquette val…
Coupled Majorana modes in a dual vortex of the Kitaev honeycomb model
Saha Institute of Nuclear Physics（萨哈核物理研究所）；Institute of Nuclear Physics, Polish Academy of Sciences（波兰科学院核物理研究所）；Sorbonne Université（索邦大学）；Université Paris-Saclay（巴黎-萨克雷大学）
We propose that spin-fluctuation-mediated spin-triplet superconductivity may be realized in repulsive Hubbard models with disconnected Fermi surfaces. The idea is confirmed for Hubbard models on triangular (dilute band filling) and honeycomb (near half-filling) lattices using fluctuation exchange approximation, where triplet pairing order parameter with f-wave symmetry is obtained. Possible relevance to real superconductors is suggested.
We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=κJ_1>0$ ($J_{1}>0$) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for $κ_{c_1}<κ<κ_{c_2}$, where $κ_{c_1} \approx 0.207 \pm 0.003$ and $κ_{c_2} \approx 0.385 \pm 0.010$. The transition at $κ_{c_1}$ to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow…
We report the magnetic structure and electronic properties of the honeycomb antiferromagnet $\rm NaNi_2BiO_{5.66}$. We find magnetic order with moments along the $c$ axis for temperatures below $T_{c1}=6.3(1)\>{\rm K}$ and then in the honeycomb plane for $T < T_{c2}=4.8(1)\>{\rm K}$ with a counterrotating pattern and an ordering wave vector ${\bf q}=(\frac{1}{3},\> \frac{1}{3},\> 0.15(1))$. Density functional theory and electron spin resonance indicate this is high-spin Ni$^{3+}$ magnetism near a high to low spin transition. The ordering wave vector, in-plane magnetic correlations, missing ent…
Motivated by the rich physics of honeycomb magnetic materials, we obtain the phase diagram and analyze magnetic properties of the spin-1/2 and spin-1 J1-J2-J3 Heisenberg model on the honeycomb lattice. Based on the SU(2) and SU(3) symmetry representations of the Schwinger boson approach, which treats disordered spin liquids and magnetically ordered phases on an equal footing, we obtain the complete phase diagrams in the (J2,J3)plane. This is achieved using a fully unrestricted approach which does not assume any pre-defined Ansatze. For S=1/2, we find a quantum spin liquid (QSL) stabilized betw…
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 th…
We study numerically a bosonic analog of the Kitaev honeycomb model, which is a minimal model for $4d^4/5d^4$ quantum magnets with honeycomb lattice geometry. We construct its phase diagram by a combination of Landau theory analysis and quantum Monte Carlo simulations. In particular, we show that the phase boundaries between the paramagnetic state and magnetically ordered states are generically fluctuation-induced first order phase transitions. Our results are potentially applicable to Ru$^{4+}$- and Ir$^{5+}$-based honeycomb magnets.
SU(N) symmetric fermions on a lattice, which can be realized in ultracold-atom-based quantum simulators, have very promising prospects for realizing exotic states of matter. Here we present the ground state phase diagram of the repulsive SU(3) Hubbard model on a honeycomb lattice at 1/3 filling obtained from infinite projected entangled pair states tensor network calculations. In the strongly interacting limit the ground state has plaquette order. Upon decreasing the interaction strength $U/t$ we find a first order transition at $U/t=7.2(2)$ into a dimerized, color-ordered state, which extends…
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group (DMRG) simulation, we identify a metal-insulator transition around $U_c/t=2.5\sim3$. In the vicinity of $U_c$, we find strong spin/orbital density wave fluctuations at commensurate wavevectors, accompanied by weaker incommensurate charge density wave (CDW) fluctuations. The spin/orbital density wave fluctuations are enhanced with increasing syst…
We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half-filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a dire…
The simplest quantum generalization of the six-vertex model describes fluctuations of the order parameter of the d-density wave (DDW), believed to compete with superconductivity in the high-Tc superconductors. The ground state of this model undergoes a first order transition from the DDW phase to a resonating plaquette phase as the quantum fluctuations are increased, which is explored with the help of quantum Monte Carlo simulations and analytic considerations involving the n-vector (n=2) model with cubic anisotropy. In addition to finding a new quantum state, we show that the DDW is robust ag…
We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice combining the cellular dynamical mean-field theory and its real space extension with analytical approaches. We provide a thorough analysis of the phase diagram and temperature effects at weak spin-orbit coupling. We systematically discuss the stability of the quantum spin Hall phase toward interactions and lattice anisotropy resulting in the plaquette-honeycomb model. We also show the evolution of the helical edge states characteristic of quantum spin Hall insulators as a functi…
A microscopic theory of electronic spectrum and superconductivity within the $t$-$J$ model on the honeycomb lattice is formulated. The Dyson equation for the normal and anomalous Green functions for the two-band model in terms of the Hubbard operators is derived by applying the Mori-type projection technique. The self-energy is evaluated in the self-consistent Born approximation for electron scattering on spin and charge fluctuations induced by the kinematical interaction for the Hubbard operators. Superconducting pairing mediated by the antiferromagnetic exchange and spin fluctuations is disc…
We use density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-1/2 Heisenberg model on 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 width slightly over 15 lattice spacings and torus up to the size N=2*6*6. With increasing J2, we find a Neel phase with vanishing spin gap and a plaquette valence-bond (PVB) phase with non-zero spin gap. By extrapolating the…
The spin-3/2 Heisenberg antiferromagnet on the bilayer honeycomb lattice is a minimal model to describe the magnetic behavior of Bi$_3$Mn$_4$O$_{12}$(NO$_3$). We study this model with frustrating inter-layer second-neighbor couplings, taking into account quantum and thermal fluctuations. We use a path integral formulation in terms of coherent states to describe the low energy physics of the model. We show that for a particular point in the parameter space, close to the experimental estimated couplings, a continuum classical degeneracy is lifted by both quantum and thermal fluctuations, and a c…
We investigate the zero-temperature phase diagram of the fully frustrated transverse field Ising model on the square lattice both in the classical limit and in the presence of quantum fluctuations. At the classical level (the limit of infinite spin $S$), we find that upon decreasing the transverse field $Γ$ this model exhibits a phase transition from the fully polarized state into an eight-fold degenerate translational symmetry breaking state. This phase can be identified to correspond to plaquette order in the dimer language and remains the lowest-energy state in the entire range of fields be…
By using a variational Monte Carlo technique based upon Gutzwiller-projected fermionic states, we investigate the dynamical structure factor of the antiferromagnetic $S=1/2$ Heisenberg model on the honeycomb lattice, in presence of first-neighbor ($J_1$) and second-neighbor ($J_2$) couplings, for ${J_2 < 0.5 J_1}$. The ground state of the system shows long-range antiferromagnetic order for ${J_2/J_1 \lesssim 0.23}$, plaquette valence-bond order for ${0.23 \lesssim J_2/J_1 \lesssim 0.36}$, and columnar dimer order for ${J_2/J_1 \gtrsim 0.36}$. Within the antiferromagnetic state, a well-defined …
We show that a magnetic field in the high-symmetry direction lifts the macroscopic classical ground-state degeneracy of the honeycomb $Γ$ model and induces a long-range magnetic order. While a simple spin-polarized state is stabilized for the ferromagnetic $Γ$-exchange, a periodic $\sqrt{3}\times \sqrt{3}$ magnetic order is selected by magnetic field for the antiferromagnetic interaction. We show that the complex spin structure of the tripled unit cell can be described by the magnetization vector and a Néel order parameter, similar to those for the spin-flop state of a bipartite antiferromagne…
