We determine dynamical response functions of the S=1/2 Heisenberg quantum antiferromagnet on the kagome lattice based on large-scale exact diagonalizations combined with a continued fraction technique. The dynamical spin structure factor has important spectral weight predominantly along the boundary of the extended Brillouin zone and energy scans reveal broad response extending over a range of 2 \sim 3J concomitant with pronounced intensity at lowest available energies. Dispersive features are largely absent. Dynamical singlet correlations -- which are relevant for inelastic light probes -- reveal a similar broad response, with a high intensity at low frequencies omega/J \lesssim 0.2J. These low energy singlet excitations do however not seem to favor a specific valence bond crystal, but instead spread over many symmetry allowed eigenstates.
The $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.
The spin half Heisenberg antiferromagnet on the Kagome lattice, is mapped by Contractor Renormalization to a Spin-Pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low energy singlets observed numerically, and the non magnetic T-squared specific heat observed experimentally.
Using an advanced Monte Carlo algorithm and high precision spin dynamics simulation, we investigated the dynamical behavior of the Heisenberg antiferromagnet on a kagome lattice at extremely low temperatures. We demonstrate that the detection and correct identification of propagating excitations depends crucially on the choice of coordinates and we show how modes are displaced in Fourier space if a single, global Cartesian coordinate system is chosen.
The effect of the quenched bond-randomness on the ordering of the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice is investigated by means of an exact-diagonalization method. When the randomness exceeds a critical value, the ground state of the model exhibits a transition within the non-magnetic state into the randomness-relevant gapless spin-liquid state. Implications to the S=1/2 kagome-lattice antiferromagnet herbertsmithite is discussed.
We discuss the ground state and the low-lying excitations of the spin-half Heisenberg antiferromagnet on the two-dimensional square-kagome lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is known also for the Heisenberg antiferromagnet on the kagome and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet likely with a finite spin gap and with a large number of non-magnetic excitations within this gap. The magnetization versus field curve sho…
Low energy spectrum of the S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of exact diagonalization and the cluster expansion. The magnitude of the energy gap of the magnetic excitation is consistent with the recent experimental observation for \mpynn. In contrast to the $S=1/2$ KHAF, the non-magnetic excitations have finite energy gap comparable to the magnetic excitation. As a physical picture of the ground state, the hexagon singlet solid state is proposed and verified by variational analysis.
We investigate the effect of geometrical frustration on the $H$--$T$ phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagome lattices. The phase diagrams for the two models are obtained from large scale Monte Carlo simulations. For the kagome antiferromagnet thermal fluctuations are unable to lift completely degeneracy and stabilize translationally disordered multipolar phases. We find a substantial difference in the temperature scales of the order by disorder effect related to different degeneracy of the low- and the high-field classical ground states in the kagom…
The magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1/3 plateau are obtained by using the approximated state in the unit cell and compared with the nu- merical results of the exact diagonalization of 42 sites.
The magnetization process of the S=1 and 1/2 kagome Heisenberg antiferromagnet is studied by means of the numerical exact diagonalization method. It is found that the magnetization curve at zero temperature has a plateau at 1/3 of the full magnetization. In the presence of $\sqrt{3} \times \sqrt{3}$ lattice distortion, this plateau is enhanced and eventually the ferrimagnetic state is realized. There also appear the minor plateaux above the main plateau. The physical origin of these phenomena is discussed.
The ground state phase transition in the distorted S=1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of the perturbational calculation and numerical exact diagonalization method. For strong $\sqrt{3} \times \sqrt{3}$ lattice distortion, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and new singlet state, large HSS (LHSS) state, which is globally different from the HSS state is realized. The quantum phase transition between these two singlet states is analogous to the Haldane-dimer transition in the S=1 antiferromagnetic Heisenberg chain. The pres…
Low-energy degrees of freedom of a spin-1/2 kagome antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows to obtain quantitative description of the magnetothermodynamics of a quantum kagome antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.
We compute the magnetic susceptibility and specific heat of the spin-1/2 Heisenberg model on the kagome lattice with high-temperature expansions and exact diagonalizations. We compare the results with the experimental data on ZnCu3(OH)6Cl2 obtained by Helton et al. [Phys. Rev. Lett. 98, 107204 (2007)]. Down to k_BT/J~0.2, our calculations reproduce accurately the experimental susceptibility, with an exchange interaction J~190K and a contribution of 3.7% of weakly interacting impurity spins. The comparison between our calculations of the specific heat and the experiments indicate that the low-t…
We compute specific heat of the antiferromagnetic spin-1/2 Heisenberg model on the kagome lattice. We use a recently introduced technique to analyze high-temperature series expansion based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. In the case of kagome-lattice antiferromagnet, this method predicts a low-temperature peak at T/J<0.1.
Classical Heisenberg antiferromagnets on two-dimensional kagome and three-dimensional hyperkagome lattices are investigated by Monte Carlo simulations. For both models the symmetry-breaking states at low temperatures are described by non-zero octupole moments or third-rank spin tensor order parameters. In the case of the two-dimensional kagome antiferromagnet, a sharp crossover into a coplanar state takes place at T_k ~ 0.004J, which we attribute to proliferation of fractional vortices. The three-dimensional model exhibits a first-order transition at T_c ~ 0.002J into a phase with critical spi…
An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet on the Kagome lattice with nearest-neighbor interactions. We observe five plateaus in the magnetization curve of the diluted antiferromagnet when a magnetic field is applied which is in agreement with Monte Carlo calculation. The effect of the site-dilution on the magnetic susceptibility is also investigated and discussed. In particular, we have found that the frustrated Kagome lattice inverse susceptibility fall to zero at $0$K.
The thermal order by disorder effect in magnetic field is studied for a classical Heisenberg antiferromagnet on the kagome lattice. Using analytical arguments we predict a unique H-T phase diagram for this strongly frustrated magnet: states with a coplanar and a uniaxial triatic order parameters respectively at low and high magnetic fields and an incompressible collinear spin-liquid state at a one-third of the saturation field. We also present the Monte Carlo data which confirm existence of these phases.
Asymmetric destruction of the one-third magnetization plateau upon heating is found in the spin-1/2 kagome Heisenberg antiferromagnets using the typical pure quantum state approach. The asymmetry originates from larger density of states of low-lying excited sates of $N_{\rm s}$ spin systems with magnetization $(1/3-2/N_{\rm s})$ than that of low-lying sates with magnetization $(1/3+2/N_{\rm s})$. The enhanced specific heat and entropy that reflect the larger density of states in the lower-field side of the plateau are detectable in candidate materials of the kagome antiferromagnets. We discuss…
The ground state phase transitions in the distorted S=1 kagome Heisenberg antiferromagnet (KHAF) with single-site anisotropy D are studied by the numerical exact diagonalization method. For strong easy plane anisotropy, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and large-D state is realized. The quantum phase transition between these two states is analogous to the Haldane-large-D transition in the S=1 antiferromagnetic Heisenberg chain. The combined effect of the sqrt(3) times sqrt(3) lattice distortion and single site anisotropy is also investigated. The g…
We study the ground-state properties of the S=1/2 Heisenberg models on the quasi-onedimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We fi…
Frustrated quantum spin systems such as the Heisenberg and Kitaev models on various lattices, have been known to exhibit various exotic properties not only at zero temperature but also for finite temperatures. Inspired by the remarkable development of the quantum frustrated spin systems in recent years, we investigate the finite-temperature properties of the $S=1/2$ Kitaev-Heisenberg models on kagome and triangular lattices by means of finite-temperature Lanczos methods with improved accuracy. In both lattices, multiple peaks are confirmed in the specific heat. To find the origin of the multip…
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 introduce a two dimensional network of corner-sharing triangles with square lattice symmetry. Properties of magnetic systems here should be similar to those on the kagome lattice. Focusing on the spin half Heisenberg quantum antiferromagnet, we generalise the spin symmetry group from SU(2) to SU(N). In the large N limit, we map the model exactly to the eight vertex model, solved by Baxter. We predict an exponential number of low-lying singlet states, a triplet gap, and a two-peak specific heat. In addition, the large N limit suggests a finite temperature phase transition into a phase with o…
Ever since the experiments which founded the field of highly frustrated magnetism, the kagome Heisenberg antiferromagnet has been the archetypical setting for the study of fluctuation induced exotic ordering. To this day the nature of its classical low-temperature state has remained a mystery: the non-linear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature. Here we present an efficient Monte Carlo algorithm which remo…
The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order paramet…
We study the Heisenberg model on the pinwheel distorted kagome lattice as observed in the material Rb_2Cu_3SnF_12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based, zero-temperature, numerical linked cluster expansion to study the approach of the pinwheel distorted lattice to the uniform kagome-lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the kagome-lattice Heisenberg model is likely…
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…
The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S=1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.
We study the system size dependence of the singlet-triplet excitation gap in the $S=1/2$ kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.
We investigate the $S=1/2$ quantum spin antiferromagnets on the triangular and Kagome lattices in magnetic field, using the numerical exact diagonalization. Particularly we focus on an anomalous magnetization behavior of each system at 1/3 of the saturation magnetization. The critical exponent analyses suggest that it is a conventional magnetization plateau on the triangular lattice, while an unconventional phenomenon, called the magnetization ramp, on the Kagome lattice.
A brief review is provided of earlier work on the low temperature phases of $S=1$ kagome and triangular lattice antiferromagnets in which there is sufficiently strongly single-ion anisotropy $D$ that dominates over the antiferromagnetic exchange $J$.
The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".
Spin-1/2 Heisenberg model on kagome lattice is a typical frustrated quantum spin system. A basic structure of kagome lattice is also present in kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-1/2 Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions by the density-matrix renormalization group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking either translati…
We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system…
The anyonic excitations of a spin-liquid can feature fractional quantum numbers under space-group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice chiral spin liquid. We provide a method to detect these fractional quantum numbers in…
We have studied the effect of the Dzyaloshinskii-Moriya interaction on kagome Heisenberg anti-ferromagnet using Schwinger boson mean field theory (SBMFT). Within SBMFT framework, Messio et al had argued that the ground state of kagome antiferromagnet is possibly a chiral topological spin liquid (Phys. Rev. Lett. 108, 207204 (2012)). Thus, we have computed zero-temperature ground state phase diagram considering the time-reversal breaking states as well as fully symmetric Ansätze. We discuss the relevance of these results in experiments and other studies. Finally, we have computed the static and…
We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The SU(3)-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be -1.410(2) and establish the presence of a spin gap.
Motivated by recent numerical and experimental studies of the spin-1/2 Heisenberg antiferromagnet on kagome, we formulate a many-body model for fermionic spinons introduced by us earlier [Phys. Rev. Lett. 103, 187203 (2009)]. The spinons interact with an emergent U(1) gauge field and experience strong short-range attraction in the S=0 channel. The ground state of the model is generically a $Z_2$ liquid. We calculate the edge of the two-spinon continuum and compare the theory to the slave-fermion approach to the Heisenberg model.
We investigate the zero-temperature phase diagram of the nearest-neighbor kagome antiferromagnet in the presence of Dzyaloshinksii-Moriya interaction. We develop a theory for the transition between Z2 spin liquids with bosonic spinons and a phase with antiferromagnetic long-range order. Connections to recent numerical studies and experiments are discussed.
The coupled cluster method is applied to a spin-half model at zero temperature ($T=0$), which interpolates between Heisenberg antiferromagnets (HAF's) on a kagome and a square lattice. With respect to an underlying triangular lattice the strengths of the Heisenberg bonds joining the nearest-neighbor (NN) kagome sites are $J_{1} \geq 0$ along two of the equivalent directions and $J_{2} \geq 0$ along the third. Sites connected by $J_{2}$ bonds are themselves connected to the missing NN non-kagome sites of the triangular lattice by bonds of strength $J_{1}' \geq 0$. When $J_{1}'=J_{1}$ and $J_{2}…
We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
We construct a phenomenological Z_2 lattice gauge theory to describe the spin-liquid state of the S=1/2 kagome Heisenberg antiferromagnet in the sector with zero total spin. The model is a natural generalization of the Misguich-Serban-Pasquier Hamiltonian with added interactions that are strongly constrained by lattice symmetries. We are able to reproduce qualitatively many of the characteristic features observed in recent numerical studies. We also make connections to the previous works along similar lines.
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…
Highly frustrated spin systems such as the kagome lattice (KL) are a treasure trove of new quantum states with large entanglements. We thus study the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain (KSC), which is one-dimensional KL, using the density-matrix renormalization group (DMRG) method. Calculating central charge and entanglement spectrum for the KSC, we find a novel gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated by dynamical DMRG meth…
The magnetization process of the S=1/2 Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. We successfully obtain a new result of the magnetization process of a 42-site cluster in the entire range. Our analysis clarifies that the critical behavior around one-third of the height of the saturation is different from the typical behavior of the well-known magnetization plateau in two-dimensional systems. We also examine the effect of the $\sqrt{3}\times\sqrt{3}$-type distortion added to the kagome lattice. We find at one-third of the height of the s…
We consider the spin-1/2 antiferromagnetic Heisenberg model on the two-dimensional square-kagome lattice with almost dispersionless lowest magnon band. For a general exchange coupling geometry we elaborate low-energy effective Hamiltonians which emerge at high magnetic fields. The effective model to describe the low-energy degrees of freedom of the initial frustrated quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in a $z$-aligned magnetic field. For the effective model we perform quantum Monte Carlo simulations to discuss the low-temperature properties of the squa…
We study the magnetization process of the spin-$1/2$ Heisenberg antiferromagnet on a distorted square-kagome lattice by the numerical-diagonalization method. The magnetization jump at one-third of the height of the saturation is examined in detail; we find that the jump becomes larger when a small distortion is switched on and that it is accompanied by an abrupt change in lines along microscopic spin directions. Our finite-size results successfully confirm that the magnetization jump in a spin-isotropic system is a macroscopic jump that survives in the thermodynamic limit and that the changes …
Motivated by recent experimental work on FeCrAs, we study the magnetic properties of classical spin models on the hexagonal Fe$_2$P/ZrNiAl structure (space group $P{\bar{6}}2m$). When both transition metal/rare earth sites carry magnetic moments, one has alternating distorted kagome and triangular lattice layers. Each point of the triangular lattice lies at the centre of a distorted hexagon and actually corresponds to three isolated magnetic atoms: a "trimer". We show that a simple model consisting of antiferromagnetically correlated Heisenberg spins on the frustrated distorted kagome lattice …
A preponderance of evidence suggests that the ground state of the nearest-neighbor $S = 1/2$ antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, $D_c/J \simeq 0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need t…
Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose …
In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies [Hiroi et al.,2001]. It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the Sp(N) symmetric generalisation of this model in the large N limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagn…
Within the t-J model, we study the electronic properties of the doped antiferromagnet on the kagome lattice based on the framework of the self-consistent mean-field theory. At the half-filling, the spin-liquid ground-state energy per site of the kagome antiferromagnet is Eg/NJ=-0.859, which is in very good agreement with the numerical estimates. Away from the half-filling, the electron photoemission spectroscopy and density of states are discussed, and the results indicate that there is a gap in the normal-state of the system.
This paper is concerned with physics of the low energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases - an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the o…
The frustration of antiferromagnetic interactions on the loosely connected kagome lattice associated to the enhancement of quantum fluctuations for S=1/2 spins was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be synthesized and enables a close comparison to theories. We review and classify various experimental results obtained over the past years and underline some of the pending issues.
Employing complementary torque magnetometry and electron spin resonance on single crystals of herbertsmithite, the closest realization to date of a quantum kagome antiferromagnet featuring a spin-liquid ground state, we provide novel insight into different contributions to its magnetism. At low temperatures, two distinct types of defects with different magnetic couplings to the kagome spins are found. Surprisingly, their magnetic response contradicts the three-fold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establi…
The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on the Kagome lattice is described by a quantitative Quantum Dimer Model. Using advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal order with a large 36-site unit cell and hidden degeneracy between even and odd parities. Evidences are given that this groundstate lies in the vicinity of a $\mathbb{Z}_2$ dimer liquid region separated by a Quantum Critical Point. Implications regarding numerical analysis and experiments are discussed.
The recent NMR experiments on ZnCu3(OH)6Cl2 motivate our study of the effect of non- magnetic defects on the antiferromagnetic spin-1/2 kagome lattice. We use exact diagonalization methods to study the effect of two such defects on finite size systems. Our results, obtained without adjustable parameters, are in good quantitative agreement with recent Oxygen 17 NMR data. They provide support for the experimental interpretation of the presence of defects within the kagome layers due to Zn/Cu substitutions. Our results also show that disorder effects become relevant at lower temperatures, raising…
We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks do…
Motivated by the unabating interest in the spin-1/2 Heisenberg antiferromagnetic model on the Kagome lattice, we investigate the energetics of projected Schwinger boson (SB) wave functions in the $J_1$--$J_2$ model with antiferromagnetic $J_2$ coupling. Our variational Monte Carlo results show that Sachdev's $Q_1=Q_2$ SB ansatz has a lower energy than the Dirac spin liquid for $J_2\gtrsim 0.08 J_1$ and the ${\bf q=0}$ Jastrow type magnetically ordered state. This work demonstrates that the projected SB wave functions can be tested on the same footing as their fermionic counterparts.
We prepared a powder sample of edwardsite Cd2Cu3(SO4)2(OH)6 4H2O, which is a new candidate compound for the spin-1/2 kagome antiferromagnet, and studied its magnetic properties by magnetic susceptibility and heat capacity measurements. Edwardsite has a deformed kagome lattice with an average antiferromagnetic interaction of 51 K between nearby spins and shows an antiferromagnetic order accompanied by a small ferromagnetic moment below 4.3 K. The weak ferromagnetism is likely due to spin canting caused by sizable Dzyaloshinsky-Moriya interactions, which may stabilize the long-range magnetic ord…
