Gapped 1/9 Magnetization Plateau in the Anisotropic Kagome Antiferromagnet Y-kapellasite
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Laboratoire de Physique des Solides（固体物理实验室）；Clarendon Laboratory, Department of Physics, University of Oxford（牛津大学克拉伦登实验室物理系）；Department of Physics, University of Warwick（华威大学物理系）；Physikalisches Institut, Goethe-Universität Frankfurt（法兰克福歌德大学物理研究所）；Laboratoire National des Champs Magnétiques Intenses, LNCMI-CNRS (UPR3228), EMFL, Univ. Grenoble Alpes, Univ. Toulouse, INSA-T（强磁场国家实验室，LNCMI-CNRS (UPR3228)，欧洲强磁场联合实验室，格勒诺布尔阿尔卑斯大学，图卢兹大学，INSA-T）；Max-Planck-Institute for So（马克斯·普朗克研究所）
Dipranjan Chatterjee, Paul A. Goddard, Ewan R. P. Thomas, Katharina M. Zoch, Hank C. H. Wu, Benjamin M. Huddart, Cornelius Krellner, Edwin Kermarrec, Mladen Hor… 展开作者
Dipranjan Chatterjee, Paul A. Goddard, Ewan R. P. Thomas, Katharina M. Zoch, Hank C. H. Wu, Benjamin M. Huddart, Cornelius Krellner, Edwin Kermarrec, Mladen Horvatić, Steffen Krämer, Pascal Puphal, John Singleton, Stephen J. Blundell, Fabrice Bert
Fractional magnetization plateaus provide a sensitive probe of many-body spin states in frustrated quantum magnets, yet their microscopic origin in kagome antiferromagnets remains unresolved. This is particularly true of the mysterious $1/9$ plateau, which is predicted by theory but infrequently observed in experiment. Here, we investigate this problem in the $S = 1/2$ anisotropic kagome antiferromagnet Y-kapellasite, Y$_3$Cu$_9$(OH)$_{19}$Cl$_8$, using pulsed-field magnetization measurements on single crystals and high-field $^{35}$Cl NMR. We identify a hierarchy of field-induced fractional features, including $1/3$ and $1/9$ plateaus, as well as a weaker low-field feature. Analysis of the NMR spectra and the magnetic susceptibility across the $1/9$ plateau demonstrate that it is accompanied by an ordered local spin configuration, a strong suppression of low-energy spin fluctuations and activated behavior, consistent with a gapped fractional state. These features differ from those in the only other material YCu$_3$(OH)$_6$Br$_2$[Br$_{1-y}$(OH)$_y$] in which this plateau is observed, implying a surprising robustness of the $1/9$ state to the details of the underlying magnetism.
The recently discovered natural minerals Cu3Zn(OH)6Cl2 and Cu3Mg(OH)6Cl2 are spin 1/2 systems with an ideal kagome geometry. Based on electronic structure calculations, we develop a realistic model which includes couplings across the kagome hexagons beyond the original kagome model that are intrinsic in real kagome materials. Exact diagonalization studies for the derived model reveal a strong impact of these couplings on the magnetic ground state. Our predictions could be compared to and supplied with neutron scattering, thermodynamic and NMR data.
Magnetic susceptibility, NMR, muSR, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphous with the herbertsmithite mineral, is a gapless spin liquid with frustrated interactions showing unusual dynamic short-range correlations of non-coplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to thermodynamical data. The experimental data are compared to theoretical calculations using the Schwinger-boson approach.
We present a method to build magnetic models for insulators based on high-temperature expansions by fitting both the magnetic susceptibility and the low temperature specific heat data. It is applied to the frustrated magnet kapellasite (Cu3Zn(OH)6Cl2) with the J1-J2-Jd-Heisenberg model on the kagome lattice. Experimental data are reproduced with a set of "competing" exchange energies closed to J1 = -12K, J2= -4K and Jd=15.6K, where Jd is the third neighbor exchange energy across the hexagon. Strong constrains between these exchange energies are established. These values confirm the results of …
We present a $^{35}$Cl NMR study for spin $S=1/2$ perfect kagome antiferromagnet Ca-kapellasite (CaCu$_{3}$(OH)$_{6}$Cl$_{2}\cdot$0.6H$_{2}$O) with a magnetic transition at $T^{\ast}=7.2$ K. The static magnetic structure in the ground state has been determined to be a chirality-ordered $Q=0$ state, which is selected by a finite Dzyaloshinskii-Moriya interaction. The low-energy magnetic excitations in the ordered state are investigated by the nuclear spin-lattice relaxation rate measurement. We detect a weakly temperature dependent contribution in the magnetic fluctuations perpendicular to the …
We report $^{35}$Cl NMR, ESR, $μ$SR and specific heat measurements on the $S=1/2$ frustrated kagomé magnet kapellasite, $α-$Cu$_3$Zn(OH)$_6$Cl$_2$, where a gapless spin liquid phase is stabilized by a set of competing exchange interactions. Our measurements confirm the ferromagnetic character of the nearest-neighbour exchange interaction $J_1$ and give an energy scale for the competing interactions $|J| \sim 10$ K. The study of the temperature-dependent ESR lineshift reveals a moderate symmetric exchange anisotropy term $D$, with $|D/J|\sim 3$%. These findings validate a posteriori the use of …
The search for the resonating valence bond (RVB) state continues to underpin many areas of condensed matter research. The RVB is made from the dimerisation of spins on different sites into fluctuating singlets, and was proposed by Anderson to be the reference state from which the transition to BCS superconductivity occurs. Little is known about the state experimentally, due to the scarcity of model materials. Theoretical work has put forward the S = 1/2 kagome antiferromagnet (KAFM) as a good candidate for the realization of the RVB state. In this paper we introduce a new model system, the S =…
A clear thermal Hall signal ($κ_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagomé antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2\cdot 0.6$H$_2$O). We found that $κ_{xy}$ is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J \sim 0.1$. In particular, $κ_{xy}$ values of Ca kapellasite and those of another kagomé antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $κ_{xy}$ fo…
We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings Jhexagon, J and J', and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear Q = 0 magnetic phase, two unusual non-collinear coplanar Q = (1/3,1/3) phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-di…
We have investigated the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field suppression effect on the longitudinal thermal conductivity k_xx sets in below ~25 K, suggesting a large spin contribution k_xx^sp in k_xx. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity k_xy shows a significant dependence on the sample's scattering time. On the other hand, the temperature dependence of k_xy is similar in all Cd-K samples; k_xy shows a peak at almost the same tempera…
Recent discoveries in neutron scattering experiments for Kapellasite and Herbertsmithite as well as theoretical calculations of possible spin liquid phases have revived interest in magnetic phenomena on the kagome lattice. We study the quantum phase diagram of the S=1/2 Heisenberg kagome model as a function of nearest neighbor coupling J1 and second neighbor coupling J2. Employing the pseudofermion functional renormalization group, we find four types of magnetic quantum order (q=0 order, cuboc order, ferromagnetic order, and Sqrt{3}x\Sqrt{3} order) as well as extended magnetically disordered r…
Motivated by recent experiments on the Heisenberg S=1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional…
Ab Initio Investigation of Pressure Effects in the Spin-Liquid Candidate Y-Kapellasite
European Synchrotron Radiation Facility（欧洲同步辐射装置）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Institut für Theoretische Physik, Goethe-Universitat Frankfurt（法兰克福歌德大学理论物理研究所）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
Herbertsmithite (ZnCu3(OH)6Cl2) is often discussed as the best realization of the highly frustrated antiferromagnetic kagome lattice known so far. We employ density functional theory calculations to determine eight exchange coupling constants of the underlying Heisenberg Hamiltonian. We find the nearest neighbour coupling J1 to exceed all other couplings by far. However, next-nearest neighbour kagome layer couplings of 0.019 J1 and interlayer couplings of up to -0.035 J1 slightly modify the perfect antiferromagnetic kagome Hamiltonian. Interestingly, the largest interlayer coupling is ferromag…
Using a perturbative renormalization group approach, we show that the extended ($J_1$-$J_2$-$J_d$) Heisenberg model on the kagome lattice with a staggered chiral interaction ($J_χ$) can exhibit a gapless chiral quantum spin liquid phase. Within a coupled-chains construction, this phase can be understood as a chiral sliding Luttinger liquid with algebraic decay of spin correlations along the chain directions. We calculate the low-energy properties of this gapless chiral spin liquid using the effective field theory and show that they are compatible with the predictions from parton mean-field the…
Spin-1/2 magnets with kagome geometry, being for years a generic object of theoretical investigations, have few real material realizations. Recently, a DFT-based microscopic model for two such materials, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, was presented [O. Janson, J. Richter and H. Rosner, arXiv:0806.1592]. Here, we focus on the intrinsic properties of real spin-1/2 kagome materials having influence on the magnetic ground state and the low-temperature excitations. We find that the values of exchange integrals are strongly dependent on O--H distance inside the hydroxyl group…
Frustrated magnetism on the kagome lattice has been a fertile ground for rich and fascinating physics, ranging from experimental evidence of a spin liquid to theoretical predictions of exotic superconductivity. Among experimentally realized spin-$\frac{1}{2}$ kagome magnets, herbertsmithite, kapellasite, and haydeeite [(Zn,Mg)Cu$_{3}$(OH)$_{6}$Cl$_{2}$] are all well described by a three-parameter Heisenberg model, but they exhibit distinctly different physics. We address the problem using a pseudofermion functional renormalization-group approach and analyze the low-energy physics in the experi…
Search for a new quantum state of matter emerging in a crystal is one of recent trends in condensed matter physics. For magnetic materials, geometrical frustration and high magnetic field are two key ingredients to realize it: a conventional magnetic order is possibly destroyed by competing interactions (frustration) and is replaced by an exotic state that is characterized in terms of quasiparticles, that are magnons, and the magnetic field can control the density and chemical potential of the magnons. Here we show that a synthetic copper mineral, Cd-kapellasite, comprising a kagome lattice ma…
We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code…
We argue that a relatively simple model containing only SU(2)-invariant chiral three-spin interactions on a Kagome lattice of S=1/2 spins can give rise to both a gapped and a gapless quantum spin liquid. Our arguments are rooted in a formulation in terms of network models of edge states and are backed up by a careful numerical analysis. For a uniform choice of chirality on the lattice, we realize the Kalmeyer-Laughlin state, i.e. a gapped spin liquid which is identified as the nu=1/2 bosonic Laughlin state. For staggered chiralities, a gapless spin liquid emerges which exhibits gapless spin ex…
We report a new kagome quantum spin liquid candidate Cu$_3$Zn(OH)$_6$FBr, which does not experience any phase transition down to 50 mK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature ($\sim$ 200 K). A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from $^{19}$F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologicall…
We report on the low-energy dynamics in the kagome antiferromagnet CaCu$_3$(OD)$_6$Cl$_2\cdot0.6$D$_2$O (Ca-kapellasite) as studied by use of $^2$D-NMR measurements. Previous $^{35}$Cl-NMR measurements revealed that the nuclear spin-lattice relaxation rate ($1/T_1$) shows two peaks at temperatures, $T^{\ast} = 7.2$ K and $T_s \simeq 25$ K. While the low-temperature peak at $T^{\ast}$ is ascribed to the critical fluctuations near the long-range magnetic ordering, the origin of the high-temperature peak has not been fully understood. From the $1/T_1$ measurements on the D sites at the OD groups …
The nature of the ground state of the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings $J_{\vartriangle}$ and $J_{\triangledown}$ within elementary up- and down-pointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped $\mathbb{Z}_{2}$ spin liquid. For several values of the ratio $J_{\triangledown}/J_{\vartriangl…
With strong geometric frustration and quantum fluctuations, S=1/2 quantum Heisenberg antiferromagnets on the Kagome lattice has long been considered as an ideal platform to realize spin liquid (SL), a novel phase with no symmetry breaking and fractionalized excitations. A recent numerical study of Heisenberg S=1/2 Kagome lattice model (HKLM) show that in contrast to earlier studies, the ground state is a singlet-gapped SL with signatures of Z2 topological order. Motivated by this numerical discovery, we use projective symmetry group to classify all 20 possible Schwinger-fermion mean-field stat…
We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the sim…
Based on large-scale quantum Monte Carlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice quantum spin-$1/2$ model, which is known to harbor an extended $Z_2$ quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit-cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the $Z_2$ quantum spin l…
The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin-liquid ground state. The nature of its ground state remains a matter of great debate. We conducted 17-O single crystal NMR measurements of the S=1/2 kagome lattice in herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrate that the intrinsic local spin susceptibility $χ_{kagome}$ deduced from the 17-O NMR frequency shift asymptotes to zero below temperature T ~ 0.03 J, where J ~ 200 K is the Cu-Cu super-exc…
We report variational Monte Carlo calculations for the spin-$\frac{1}{2}$ Heisenberg model on the kagome lattice in the presence of both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic superexchange couplings. Our approach is based upon Gutzwiller projected fermionic states that represent a flexible tool to describe quantum spin liquids with different properties (e.g., gapless and gapped). We show that, on finite clusters, a gapped $\mathbb{Z}_{2}$ spin liquid can be stabilized in the presence of a finite $J_2$ superexchange, with a substantial energy gain with respect…
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 Néel antiferromagnetic order survives only in a small…
In a recent paper [arXiv:1601.02165], Tao Li claimed that a gapped $\mathbb{Z}_2$ spin liquid, obtained using projected Gutzwiller fermionic wave functions, can be stabilized in the Heisenberg model on the kagome lattice. We perform very accurate variational calculations and confirm with unprecedented accuracy the fact, that the $\mathbb{Z}_{2}$ spin liquid is a local energy minimum that goes away with system size, thus reaffirming the scenario of a gapless $U(1)$ Dirac spin liquid ground state.
A novel cuprate Volborthite, Cu3V2O7(OH)2-2H2O, containing an S-1/2 (Cu 2+ spin) kagome-like lattice is studied by magnetic susceptibility, specific heat, and 51 V NMR measurements. Signs for neither long-range order nor spin-gapped singlet ground states are detected down to 1.8 K, in spite of large antiferromagnetic couplings of ~100 K between Cu spins forming a two-dimensional kagome-like network. It is suggested that Volborthite represents a system close to a quantum critical point between classical long-range ordered and quantum disordered phases.
We study an exactly solvable quantum spin model of Kitaev type on the kagome lattice. We find a rich phase diagram which includes a topological (gapped) chiral spin liquid with gapless chiral edge states, and a gapless chiral spin liquid phase with a spin Fermi surface. The ground state of the current model contains an odd number of electrons per unit cell which qualitatively distinguishes it from previously studied exactly solvable models with a spin Fermi surface. Moreover, we show that the spin Fermi surface is stable against weak perturbations.
In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped $\mathbb{Z_2}$ spin liquids.
Entanglement renormalization techniques are applied to numerically investigate the ground state of the spin-1/2 Heisenberg model on a kagome lattice. Lattices of N={36,144,inf} sites with periodic boundary conditions are considered. For the infinite lattice, the best approximation to the ground state is found to be a valence bond crystal (VBC) with a 36-site unit cell, compatible with a previous proposal. Its energy per site, E=-0.43221, is an exact upper bound and is lower than the energy of any previous (gapped or algebraic) spin liquid candidate for the ground state.
We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, le…
Quantum spin ice, modeled for magnetic rare-earth pyrochlores, has attracted great interest for hosting a U(1) quantum spin liquid, which involves spin-ice monopoles as gapped deconfined spinons, as well as gapless excitations analogous to photons. However, the global phase diagram under a [111] magnetic field remains open. Here we uncover by means of unbiased quantum Monte-Carlo simulations that a supersolid of monopoles, showing both a superfluidity and a partial ionization, intervenes the kagomé spin ice and a fully ionized monopole insulator, in contrast to classical spin ice where a direc…
Motivated by recent density-matrix renormalization group (DMRG) calculations [Yan, Huse, and White, Science 332, 1173 (2011)], which claimed that the ground state of the nearest-neighbor spin-1/2 Heisenberg antiferromagnet on the kagome lattice geometry is a fully gapped spin liquid with numerical signatures of Z2 gauge structure, and a further theoretical work [Lu, Ran, and Lee, Phys. Rev. B 83, 224413 (2011)], which gave a classification of all Schwinger-fermion mean-field fully symmetric Z2 spin liquids on the kagome lattice, we have thoroughly studied Gutzwiller-projected fermionic wave fu…
We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-$1/2$ quantum Heisenberg model on the kagome lattice. Starting from the algebraic $U(1)$ Dirac spin liquid state proposed by Y. Ran $et al.$ [Phys. Rev. Lett. $98$, $117205$ ($2007$)] and iteratively applying a few Lanczos steps, we compute the lowest $S=2$ excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance…
We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation functions and finite topological entanglement gamma consistent with gamma=ld 2, ruling out gapless, ch…
We calculate dynamical spin structure factors for gapped chiral spin liquid states in the spin-1/2 Heisenberg antiferromagnet on the kagome lattice using Schwinger-boson mean-field theory. In contrast to static (equal-time) structure factors, the dynamical structure factor shows clear signatures of time-reversal symmetry breaking for chiral spin liquid states. In particular, momentum inversion $\bm{k} \to -\bm{k}$ symmetry as well as the six-fold rotation symmetry around the $Γ$-point are lost. We highlight other interesting features, such as a relatively flat onset of the two-spinon continuum…
We report 17O NMR measurements in the S=1/2 Cu2+ kagome antiferromagnet Herbertsmithite ZnCu3(OH)6Cl2 down to 45mK in magnetic fields ranging from 2T to 12T. While Herbertsmithite displays a gapless spin-liquid behavior in zero field, we uncover an instability toward a spin-solid phase at sub-kelvin temperature induced by an applied magnetic field. The latter phase shows largely suppressed moments $\lesssim 0.1\muB$ and gapped excitations. The H-T phase diagram suggests the existence of a quantum critical point at the small but finite magnetic field mu0 Hc=1.55(25)T. We discuss this finding in…
We study the low-energy properties of Heisenberg antiferromagnetic spin-1/2 and spin-1 systems on various clusters made up of triangles. Some of the clusters have a geometry similar to representative pieces of the Kagome lattice, while others have the geometry of a sawtooth chain. While the ground state always has the lowest possible spin (0 or 1/2), the nature of the low-energy excitations depends on the geometry and the site spin. For the Kagome clusters with spin-1 sites, the lowest excitations are gapped, with singlet and triplet excitations having similar gaps. This is in contrast to Kago…
We discuss the ground-state degeneracy of spin-$1/2$ kagome-lattice quantum antiferromagnets on magnetization plateaus by employing two complementary methods: the adiabatic flux insertion in closed boundary conditions and a 't Hooft anomaly argument on inherent symmetries in a quasi-one-dimensional limit. The flux insertion with a tilted boundary condition restricts the lower bound of the ground-state degeneracy on $1/9$, $1/3$, $5/9$, and $7/9$ magnetization plateaus under the $\mathrm{U(1)}$ spin-rotation and the translation symmetries: $3$, $1$, $3$, and $3$, respectively. This result motiv…
Motivated by recent experiments on the vanadium oxyfluoride material DQVOF, we examine possible spin liquid phases on a breathing kagome lattice of S=1/2 spins. By performing a projective symmetry group analysis, we determine the possible phases for both fermionic and bosonic $\mathbb{Z}_2$ spin liquids on this lattice, and establish the correspondence between the two. The nature of the ground state of the Heisenberg model on the isotropic kagome lattice is a hotly debated topic, with both $\mathbb{Z}_2$ and U(1) spin liquids argued to be plausible ground states. Using variational Monte Carlo …
Recent experiments on the "hyper-kagome" lattice system Na$_4$Ir$_3$O$_8$ have demonstrated that it is a rare example of a three dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary mechanism lifting the macroscopic degeneracy inherited by classical spins on this lattice. In the semi-classical limit we predict, based on large-N calculations, that an unusual $\vec q=0$ coplaner magnetically ordered ground state is stabilized with no local "weather vane" modes. This phase melts in the quantum limit and a gapped topological Z$_2$ spin liq…
There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appear to be a plethora of low energy excitations, predominantly singlets but also spin carrying, which suggest that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we de…
Herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$, is a two dimensional kagomé lattice realization of a spin liquid, with evidence for fractionalized excitations and a gapped ground state. Such a quantum spin liquid has been proposed to underlie high temperature superconductivity and is predicted to produce a wealth of new states, including a Dirac metal at $1/3$rd electron doping. Here we report the topochemical synthesis of electron-doped ZnLi$_x$Cu$_3$(OH)$_6$Cl$_2$ from $x$ = 0 to $x$ = 1.8 ($3/5$th per Cu$^{2+}$). Contrary to expectations, no metallicity or superconductivity is induced. Instead, we…
We report the local probe investigation of a frustrated antiferromagnet Pr$_3$BWO$_9$ with the distorted kagome lattice. Absence of magnetic order or spin freezing is indicated by the spectral analysis down to 0.3 K and specific heat measurements down to 0.09 K. The Knight shifts show an upturn behavior with the sample cooling down, which is further suppressed by external field. For the spin dynamics, gapped spin excitation is observed from the temperature dependence of spin-lattice relaxation rates, with the gap size proportional to the applied magnetic field intensity. Comparatively, an unex…
We show that the best variational ground state of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model with nearest-neighboring exchange coupling(NN-KAFH) is a $Z_{2}$ spin liquid state, rather than the widely believed $U(1)$ Dirac spin liquid state. The spinon excitation in the $Z_{2}$ spin liquid state has a small gap of about $1/40$ of the spinon band width. We find that while the $Z_{2}$ and the $U(1)$ spin liquid state have a large overlap on finite clusters and are thus very close in energy, they host totally different spinon excitation spectrum. The strength of the RVB theor…
The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets. But the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite ZnCu$_{3}$(OD)$_{6}$FBr and herbertsmithite ZnCu$_{3}$(OD)$_{6}$Cl$_2$ do not exhibit long range order, and they are considered the best realizations of t…
Optimizing translationally invariant infinite-Projected Entangled Pair States (iPEPS), we investigate the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) and spin-1 Heisenberg models on the Kagome lattice as a function of magnetic field. We found that the magnetization curves offer a wide variety of compressible and incompressible phases. Incompressible nematic phases breaking the lattice $C_3$ rotation -- for which we propose simple qualitative pictures -- give rise to magnetization plateaux at reduced magnetization $m_z=5/6$ and $m_z=1/3$ for spin-2 and spin-1, respectively, in addition to the $m_…
We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site {$e_0=-1.41090(2)$ with $D^*=8$ multiplets retained (i.e., a bond dimension of $D=24$), and $e_0=-1.4116(4)$ from large-$D$ extrapolation,} by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $δ\approx$ 19\%, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer…
We study the energy and the static spin structure factor of the ground state of the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U(1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2 spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site E/J=-0.4365(2), which is equal, within three error bars, to…
We have performed large scale variational search for the best RVB ansatz for the spin-$\frac{1}{2}$ kagome antiferromagnet with both nearest-neighboring(NN) and next-nearest-neighboring(NNN) exchanges assuming only translational symmetry. We find the best RVB state is always fully symmetric and has an mean field ansatz that is gauge equivalent to a previous proposed Z$_{2}$ spin liquid ansatz. The Z$_{2}$ state is found to be slightly more stable than the extensively studied U(1) gapless Dirac spin liquid state in both the $J_{2}\neq0$ and the $J_{2}=0$ case and to possess a small spinon gap f…
The field of frustrated magnetism has been enriched significantly by the discovery of various kagome lattice compounds. These materials exhibit a great variety of macroscopic behaviours ranging from magnetic orders to quantum spin liquids. Using large-scale exact diagonalization, we construct the phase diagram of the $S=1/2$ $J_1$-$J_2$ kagome Heisenberg model with $z$-axis Dzyaloshinskii-Moriya interaction $D_z$. We show that this model can systematically account for many of the experimentally observed phases. Small $J_2$ and $D_z$ can stabilize respectively a gapped and a gapless spin liquid…
