We use the coupled cluster method to investigate the ground-state (GS) properties of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ model on the honeycomb lattice, with nearest-neighbor exchange coupling $J_1$ plus next-nearest-neighbor ($J_2$) and next-next-nearest-neighbor ($J_3$) exchanges of equal strength. In particular we find a direct first-order phase transition between the Néel-ordered antiferromagnetic phase and the ferromagnetic phase at a value $J_{2}/J_{1} = -1.17 \pm 0.01$ when $J_{1}>0$, compared to the corresponding classical value of -1. We find no evidence for any intermediate phase. From this and our previous CCM studies of the model we present its full zero-temperature GS phase diagram.
The Kitaev-Heisenberg model defined on both honeycomb and triangular lattices has been studied intensively in recent years as a possible model to describe spin-orbital physics in iridium oxides. In the model, there are many phases characteristic for each lattice. However, there is no study how the phases in the two lattices merge each other when geometry changes from honeycomb lattice to triangular lattice. We investigate the ground state of the Kitaev-Heisenberg model defined on the system connecting the honeycomb and triangular lattices, named a honeycomb-triangular lattice. We obtain a grou…
We investigate the classical phase diagram of the stuffed honeycomb Heisenberg lattice, which consists of a honeycomb lattice with a superimposed triangular lattice formed by sites at the center of each hexagon. This lattice encompasses and interpolates between the honeycomb, triangular and dice lattices, preserving the hexagonal symmetry while expanding the phase space for potential spin liquids. We use a combination of iterative minimization, classical Monte Carlo and analytical techniques to determine the complete ground state phase diagram. It is quite rich, with a variety of non-coplanar …
In extended Kitaev models on the honeycomb lattice, off-diagonal interactions (e.g. the $Γ, Γ^{'}$ terms) give rise to non-Kitaev quantum spin liquid (QSL) and several magnetically ordered phases. In the present work, we dope holes to the system and study the resultant $t$-$K$-$Γ$-$Γ^{'}$ model by mean field theory. The interplay between the charge and spin degrees of freedom results in a rich phase diagram. Similar to doped cuprates, superconductors, pseudogap phases, fermi liquid, strange metal and paramagnetic phase are generated. What is different is that, more than one superconducting pha…
Quantum Phase Transition, O(3) Universality Class and Phase Diagram of Spin-1/2 Heisenberg Antiferromagnet on Distorted Honeycomb Lattice: A Tensor Renormalization Group Study
用张量重整化群方法研究了扭曲蜂窝晶格上自旋为1/2的海森堡反铁磁体。结果表明，在耦合比α c = 0.54的临界点，体系发生了从带隙的量子二聚体相到共线Neel相的二级量子相变，得到了量子临界指数ν= 0.69（2），γ= 1.363（8）.量子临界性属于O（3）普适类。提出了场耦合比平面中的基态相图，其中确定了诸如二聚体、半经典Neel和极化相等相。本文还讨论了本自旋系统与DHC晶格上玻色子哈伯德模型之间的联系。
Motivated by the growing interest in the novel quantum phases in materials with strong electron correlations and spin-orbit coupling, we study the interplay between the spin-orbit coupling, Kondo interaction, and magnetic frustration of a Kondo lattice model on a two-dimensional honeycomb lattice. We calculate the renormalized electronic structure and correlation functions at the saddle point based on a fermionic representation of the spin operators. We find a global phase diagram of the model at half-filling, which contains a variety of phases due to the competing interactions. In addition to…
The frustrated XY model on the honeycomb lattice has drawn lots of attentions because of the potential emergence of chiral spin liquid (CSL) with the increasing of frustrations or competing interactions. In this work, we study the extended spin-$\frac{1}{2}$ XY model with nearest-neighbor ($J_1$), and next-nearest-neighbor ($J_2$) interactions in the presence of a three-spins chiral ($J_χ$) term using density matrix renormalization group methods. We obtain a quantum phase diagram with both conventionally ordered and topologically ordered phases. In particular, the long-sought Kalmeyer-Laughlin…
In this paper, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg-$Γ$ model on a honeycomb lattice by dimer series expansion and exact diagonalization. We focus on the effects of the anisotropy of the interactions; by tuning the coupling constants, the system changes between the isolated dimer and the spin-chain models. We find that, in the spin-chain limit, there are three kinds of states: a Tomonaga-Luttinger liquid and two magnetically long-range-ordered states. All three states become two-dimensional long-range ordered states by the infinitesimal interchain interaction…
Phase diagram of interacting spinless fermions on the honeycomb lattice
自2004年石墨烯被发现以来，费米子在六方晶格上的跳跃是凝聚态物质中最活跃的研究领域之一。几何和量子力学效应之间相互作用的另一个令人兴奋的方面是由Halfton模型（F。D. M. Halcester，Phys. Rev. Lett. 61，2015（1988）），其中无自旋费米子在蜂窝晶格上经历一定的通量模式导致物质的拓扑相的稳定，这与莫特绝缘体不同，并且现在被称为陈氏绝缘体。在这种情况下，它是至关重要的，以了解相互作用的作用，本次审查将描述最近的结果，已经获得了一个极小模型，即无自旋费米子费米子与最近和下一个最近的邻居密度-密度相互作用的蜂窝晶格在半填充。讨论的主题包括介绍的极小模型和狄拉克半金属的可能的不稳定性的讨论，各种理论和数值方法的介绍，并总结的结果，特别强调的稳定性或不一些奇异的量子相位，如电荷有序的（类似于维格纳晶体）或自发陈绝缘体相位。
Compounds of transition metal ions with strong spin-orbit coupling recently attracted attention due to the possibility to host frustrated bond-dependent anisotropic magnetic interactions. In general, such interactions lead to complex phase diagrams that may include exotic phases, e.g. the Kitaev spin liquid. Here we report on our comprehensive analysis of the global phase diagram of the extended Kitaev-Heisenberg model relevant to honeycomb lattice compounds Na2IrO3 and alpha-RuCl3. We have utilized recently developed method based on spin coherent states that enabled us to resolve arbitrary sp…
Lattice Wigner crystal states stabilized by long-range Coulomb interactions have recently been realized in two-dimensional moiré materials. We employ large-scale unrestricted Hartree-Fock techniques to unveil the magnetic phase diagrams of honeycomb lattice Wigner crystals. For the three lattice filling factors with the largest charge gaps, n = 2/3, 1/2, 1/3, the magnetic phase diagrams contain multiple phases, including ones with non-collinear and non-coplanar spin arrangements. We discuss magnetization evolution with external magnetic field, which has potential as an experimental signature o…
The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, multifractal analysis are employed to characterize the phase diagram. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the …
We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two $J_1$-$J_2$ spin chains coupled with $J_\perp$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: A Haldane phase, a NNN-Haldane phase and a staggered dimer phase when $J_{\perp} < 0$; a rung singlet phase and a columnar dimer phase when $J_{\perp} > 0$. An interesting r…
Recent theoretical studies have suggested that Kitaev physics and such effects as formation of a mysterious spin-liquid state can be expected not only in RuCl3 and iridates, but also in conventional $3d$ transition metal compounds. Using DC and AC magnetometry, thermodynamic and $^{23}$Na nuclear magnetic resonance measurements (NMR) we studied such a candidate material Na3Co2SbO6. A full phase diagram of Na3Co2SbO6 in a wide range of magnetic fields and temperatures is presented. The results demonstrate transformation of the antiferromagnetic structure under the external magnetic field, gradu…
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 investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, $J_{\rm A}$, $J_{\rm B}$, and $J_{\rm C}$ that is realized in a distorted honeycomb-lattice antiferromagnet ${\rm Cu_2 (pymca)_3 (ClO_4)}$. We remeasured the magnetic susceptibility of its polycrystalline sample with special care, and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the $J_{\…
The crystal structure and magnetic property of the single crystalline hexagonal rare-earth indium oxides GdInO$_3$ have been studied by combing experiments and model calculations. The two inequivalent Gd$^{3+}$ ions form the centered honeycomb lattice, which consists of honeycomb and triangular sublattices. The dc magnetic susceptibility and specific heat measurements suggest two antiferromagnetic phase transitions at $T_\textrm{N1}$ = 2.3 K and $T_\textrm{N2}$ = 1.02 K. An inflection point is observed in the isothermal magnetization curve, which implies an up-up-down phase with a 1/3 magnetiz…
We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg ($J=\cosϕ)$ and Kitaev ($K=\sinϕ$) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-$z$ , ferromagnetic-$xy$, staggered-$xy$, Néel-$z$, and two liquid states: Tomonaga-Luttinger liquid and spiral-$xy$. The two Kitaev points $ϕ=\fracπ{2}$ and $ϕ=\frac{3π}{2}$ are singular. The $ϕ$-dependent phase dia…
The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two complementary numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the qu…
The cluster slave-spin method is implemented to research the ground state properties of the honeycomb lattice Hubbard model with doping $δ$ and coupling $U$ being its parameters. At half-filling, a single direct and continuous phase transition between the semi-metal and antiferromagnetic (AFM) insulator is found at $U_{\text{AFM}}=2.43t$ that is in the Gross-Neveu-Yukawa universality class, where a relation between the staggered magnetization $M$ and the AFM energy gap $Δ_{\text{AFM}}$ is established as $M \propto Δ_{\text{AFM}}$, compared to $M \propto Δ_{\text{AFM}} ( \ln{Δ_{\text{AFM}}})^2$…
Phase diagram of a Hubbard model for Majorana fermions on the honeycomb lattice is explored using a combination of field theory, renormalization group and mean-field arguments, as well as exact numerical diagonalization. Unlike the previously studied versions of the model we find that even weak interactions break symmetries and lead to interesting topological phases. We establish two topologically nontrivial phases at weak coupling, one gapped with chiral edge modes, and the other gapless with anti-chiral edge modes. At strong coupling a mapping onto a novel frustrated spin-${1\over 2}$ model …
We consider the spin-$1/2$ XY frustrated antiferromagnetic Heisenberg honeycomb model. There is an unclear intermediate region in the ground state phase diagram of the model. The most recognized phases are the quantum spin-liquid (QSL) and the antiferromagnetic Ising ordering. From the viewpoint of the quantum correlations, the QSL phase is expected to be entangled. Motivated by this fact, we have calculated the concurrence, the quantum discord (QD), and the entanglement entropy, by using numerical Lanczos and density matrix renormalization group (DMRG) methods. Our results explicitly show tha…
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…
We study hard-core bosons on the honeycomb lattice in the presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract the phase diagram of the model in terms of the filling and the anisotropy. At half-filling we find a dimer insulator phase near maximum anisotropy that is characterized by a finite topological entanglement entropy $\ln(2)/2$, indicative of a fractional quantum Hall state for bosons. We identify the presence of edge states and derive a QMC-based method to extract and verify their chirality. Remarkably, this phase arise…
The spin$-1/2$ Heisenberg antiferromagnet on the honeycomb bilayer lattice is shown to display a rich variety of semiclassical and genuinely quantum phases, controlled by the interplay between intralayer frustration and interlayer exchange. Employing a complementary set of techniques, comprising spin rotationally invariant Schwinger boson mean field theory, bond operators, and series expansions we unveil the quantum phase diagram, analyzing low-energy excitations and order parameters. By virtue of Schwinger bosons we scan the complete range of exchange parameters, covering both long range orde…
Cascade of magnetic-field-induced quantum spin states in a spin-1 honeycomb magnet
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（合肥微尺度物质科学国家研究中心，中国科学技术大学）；School of Physics, Nanjing University of Science and Technology（南京理工大学物理学院）；National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院）；School of Physics, Hefei University of Technology（合肥工业大学物理学院）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理系）；Collaborative Innovation Center of Advanced Microstructures and Jiangsu Physical Science Research Center, Nanjing University（南京大学先进微结构协同创新中心与江苏省物理科学研究院）；Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）
We investigate the ground-state properies of the $K-Γ$ model on a honeycomb lattice using series expansions and numerical exact diagonalizations, where the model includes Kitaev ($K$) and symmetric off-diagonal ($Γ$) interactions. Starting from the weakly interacting dimers on the specific bond, we strengthen the interdimer interactions to the isotropically interacting system. We show that depending on $Γ$ and $K$, the dimer state survives up to the isotropically interacting system, where the phase transition occurs, or obeys a phase transition to a magnetically ordered state at an anisotropic…
