We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach -- i.e. a parton construction -- we obtain large overlaps with ground states of these extended Heisenberg models. We further suggest that the appearance of the chiral spin liquid in the time-reversal invariant case is linked to a classical transition line between two magnetically ordered phases.
By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY (zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning…
The theoretical description of non-Fermi liquids is among the most challenging questions in strongly correlated quantum matter. While there are many experimental candidates for such phases, few examples can be studied using controlled theoretical approaches. Here we introduce a novel conceptual perspective to analytically describe the non-Fermi liquid physics of gapless spin liquids arising in a family of two- and three-dimensional Kagome models. We first discuss a symmetry-protection mechanism that is responsible for the stability of the gapless phase. We then re-cast the two-dimensional Kago…
In the theory of quantum spin liquids, gauge fluctuations are emergent excitations at low energy. The gauge magnetic field is proportional to the scalar spin chirality, S1.(S2xS3). It is therefore highly desirable to measure the fluctuation spectrum of the scalar spin chirality. We show that in the Kagome lattice with a Dzyaloshinskii-Moriya term, the fluctuation in Sz which is readily measured by neutron scattering contains a piece which is proportional to the chirality fluctuation.
Due to an uprise in the variety of candidate compounds, kagome metals have recently gained significant attention. Among other features, kagome metals host Dirac cones as a key band structure feature away from half filling, and potentially yield an exceptionally large fine structure, beyond values found in other 2D Dirac materials such as graphene. We investigate the possibility of chiral symmetry breaking in kagome metals. Based on a heuristic lattice model, we determine the critical coupling strength and the ordering pattern by means of a Schwinger-Dyson mean-field analysis. As the leading in…
We propose in this work an effective field theory description of the chiral spin liquid state in Heisenberg spin system on kagomé lattice.To this end, we derive the low-energy effective theory of kagomé (isotropic) Heisenberg antiferromagnet around its ordered ground states found numerically and show that quantum fluctuations induced by further neighbor spin exchanges are equally strong as those from first neighbor.We use a chiral order parameter theory to argue for the occurrence of finite temperature chiral symmetry breaking transition into chiral ordered state in kagomé antiferromagnet with…
The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. In particular, the breaking of chiral (mirror) symmetry in quantum materials has been shown to have important technological applications. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids on the kagomé lattice. Such chiral spin liquids are closely tied to bosonic fractional quantum Hall states and host anyonic quasiparticles; however, their connection to nearby magnetically ordered states has remained a mystery. He…
We investigate the nature of quantum spin liquid (QSL) phase of the spin-$1/2$ nearest-neighbor XXZ antiferromagnet on the kagome lattice. Recent numerical calculations suggest that such a kagome spin liquid is insensitive to the XXZ anisotropy and is adjacent to a chiral spin liquid phase. Reformulating the problem in terms of a $U(1)$ lattice gauge theory with dynamical bosonic spinons, we propose that the kagome spin liquid can be understood as a deconfined critical phase extended by the $U(1)$ gauge fluctuation from a deconfined critical point between a symmetry-protected topological phase…
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.
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.
We study the electronic instabilities of the Hubbard model in the 1/6 hole-doped Kagome lattice using the variational cluster approach. The 1/6 hole doping is unique in the sense that the Fermi level is at the von Hove singularity and the Fermi surface has a perfect nesting. In this case, a density wave is usually realized. However, we demonstrate here that the chiral $d_{x^{2}-y^{2}}+id_{xy}$ superconducting state is most favorable when a small Hubbard interaction U(U<3.0t) is introduced, and a scalar chiral spin order is realized at large U(U>5.0t). Between them, a spin-disordered insulating…
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…
In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected $\mathbb Z_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can…
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…
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…
We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a $\mathbb Z_2\boxtimes\mathbb Z_2$ topological order to a $\mathbb Z_2$ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.
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…
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 …
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.
In this Letter, we identify a noncoplanar chiral spin texture on the distorted kagomé-lattice antiferromagnets induced by the presence of a magnetic field applied perpendicular to the distorted kagomé plane. The noncoplanar chiral spin texture has a nonzero scalar spin chirality similar to a chiral quantum spin liquid with broken time-reversal symmetry. In the noncoplanar regime we observe nontrivial topological magnetic excitations and thermal Hall response through the emergent field-induced scalar spin chirality in contrast to collinear ferromagnets in which the Dzyaloshinskii-Moriya (DM) sp…
Recent years have seen the discovery of a chiral spin liquid state - a bosonic analogue of a fractional Quantum Hall state first put forward by Kalmeyer and Laughlin in 1987 - in several deformations of the Heisenberg model on the Kagome lattice. Here, we apply state-of-the-art numerical techniques to one such model, where breaking of the time-reversal symmetry drives the system into the chiral phase. Our methods allow us to obtain explicit matrix-product state representations of the low-lying excitations of the chiral spin liquid state, including the topologically non-trivial semionic excitat…
Recent neutron scattering experiments on the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 (Herbertsmithite) provide the first evidence of fractionalized excitations in a quantum spin liquid state in two spatial dimensions. In contrast to existing theoretical models of spin liquids, the measured dynamic structure factor reveals an excitation continuum which is remarkably flat as a function of frequency and has almost no momentum dependence along several high-symmetry directions. Here we show that many experimentally observed features can be explained by the presence of topological viso…
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…
We introduce $\mathrm{Nd_{3}Sb_{3}Mg_{2}O_{14}}$ with ideal kagome lattices of neodymium ions in ABC stacking. Thermodynamic measurements show a Curie-Weiss temperature of $Θ_{CW}=-0.12~$K, a Nd$^{3+}$ spin-1/2 Kramers doublet ground state, and a second order phase transition at $T_N=0.56(2)~$K. Neutron scattering reveals non-coplanar scalar chiral ${\bf k} =0$ magnetic order with a correlation length exceeding 400 Å= 55 $a$ and an ordered moment of $1.79(5)~μ_B$. This order includes a canted ferromagnetic component perpendicular to the kagome planes favored by Dzyaloshinskii-Moriya interactio…
We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can suppport chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simon…
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.
The emergent behavior of spin liquids that are born out of geometrical frustration makes them an intriguing state of matter. We show that in the quantum kagome antiferromagnet ZnCu$_3$(OH)$_6$SO$_4$ several different correlated, yet fluctuating states exist. By combining complementary local-probe techniques with neutron scattering, we discover a crossover from a critical regime into a gapless spin-liquid phase with decreasing temperature. An additional unconventional instability of the latter phase leads to a second, distinct spin-liquid state that is stabilized at the lowest temperatures. We …
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 study quantum spin systems with a proper combination of geometric frustration, spin-orbit coupling and ferromagnetism. We argue that such a system is likely to be in a chiral spin state, a fractional quantum Hall (FQH) state for bosonic spin degrees of freedom. The energy scale of the bosonic FQH state is of the same order as the spin-orbit coupling and ferromagnetism --- overall much higher than the energy scale of FQH states in semiconductors.
The vanadium oxyfluoride [NH4]2[C7H14N][V7O6F18] (DQVOF) is a geometrically frustrated magnetic bilayer material. The structure consists of S=1/2 kagome planes of V4+ d1 ions with S=1 V3+ d2 ions located between the kagome layers. Muon spin relaxation measurements demonstrate the absence of spin freezing down to 40 mK despite an energy scale of 60 K for antiferromagnetic exchange interactions. From magnetization and heat capacity measurements we conclude that the S=1 spins of the interplane V3+ ions are weakly coupled to the kagome layers, such that DQVOF can be viewed as an experimental model…
We report muSR experiments on Mg{x}Cu{4-x}(OH)6Cl2 with x \sim 1, a new material isostructural to Herbertsmithite exhibiting regular kagome planes of spin 1/2 (Cu^{2+}), and therefore a candidate for a spin liquid ground state. We evidence the absence of any magnetic ordering down to 20 mK (\sim J/10^4). We investigate in detail the spin dynamics on well characterized samples in zero and applied longitudinal fields and propose a low T defect based interpretation to explain the unconventional dynamics observed in the quantum spin liquid phase.
We investigate the quasiparticle-mass enhancement in the Hubbard model on the frustrated kagome lattice by using a cluster extension of the dynamical mean-field theory. By analyzing the cluster density matrix, we find a hierarchy of energy scale among charge, spin, and chirality degrees of freedom. Large amount of entropy associated with the chirality is released at a much lower temperature than other energy scales for spin and charge fluctuations, leading to a sharp peak in the specific heat and the single-particle spectrum. The results manifest a generic mechanism of mass enhancement driven …
The study of electronic and magnetic properties of kagome lattice has been an active research area searching for topological phases of matters. In particular, the kagome system with transition metal stannides and etc exhibit interesting anomalous Hall effects driven by ferromagnetic or non-collinear magnetic ordering. In this paper, motivated by these pioneer works, we study strongly correlated spin-orbit coupled electrons in kagome lattice at 1/3 filling. Using both Hartree-Fock approach and effective model analysis, we report quantum phase transitions accompanied with distinct charge and mag…
Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor $S(\mathbf{q},ω)$ of spin liquid states on the kagome lattice. Spin-1 excited states in spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). FSL and RSL have low energy peaks in $S(\mathbf{q},ω)$ at $K$ points in the ext…
We revisit the description of the low-energy singlet sector of the spin-1/2 Heisenberg antiferromagnet on kagome in terms of an effective quantum dimer model. With the help of exact diagonalizations of appropriate finite-size clusters, we show that the embedding of a given process in its kagome environment leads to dramatic modifications of the amplitudes of the elementary loop processes, an effect not accessible to the standard approach based on the truncation of the Hamiltonian to the nearest-neighbour valence-bond basis. The resulting parameters are consistent with a Z$_2$ spin liquid rathe…
We address the problem of a lightly doped spin-liquid through a large-scale density-matrix renormalization group (DMRG) study of the $t$-$J$ model on a Kagome lattice with a small but non-zero concentration, $δ$, of doped holes. It is now widely accepted that the undoped ($δ=0$) spin 1/2 Heisenberg antiferromagnet has a spin-liquid groundstate. Theoretical arguments have been presented that light doping of such a spin-liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal (FL$^\ast$). Instead, we infer that the doped holes form an insulating cha…
Recent numerical studies have provided strong evidence for a gapped $Z_2$ quantum spin liquid in the kagome lattice spin-1/2 Heisenberg model. A special feature of spin liquids is that symmetries can be fractionalized, and different patterns of symmetry fractionalization imply distinct phases. The symmetry fractionalization pattern for the kagome spin liquid remains to be determined. A popular approach to studying spin liquids is to decompose the physical spin into partons obeying either bose (Schwinger bosons) or fermi (Abrikosov fermions) statstics, which are then treated within the mean-fie…
Effect of geometrical frustration in strongly-correlated metallic region is studied for the Hubbard model on the kagome lattice at half filling by a cluster extension of the dynamical mean-field theory combined with a continuous-time auxiliary-field quantum Monte Carlo method. We find that the electron correlation enhances the spin chirality in both vector and scalar channels. The chirality grows as decreasing temperature and exhibits a peak at a low temperature, indicating a new energy scale under strong correlation. The peak temperature is considerably lower than that for the local spin mome…
Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature TC up to 7K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than TC. In this work, we use scanning tunneling microscopy (STM) to study the charge order in kagome superconductor RbV3Sb5. We observe both a 2x2 chiral charge order and nematic surface superlattices (predominantly 1x4). We find that the 2x2 charge order exhibits…
The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities[1-4]. This has been suggested as the reason why it is not strongly supported in large-scale numerical calculations[5]. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks both spatial symmetry in …
We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO(3)_1$ (or, equivalently, $SU(2)_2$) field theory predictions. We propose a local H…
Low energy inelastic neutron scattering on single crystals of the kagome spin liquid compound ZnCu3(OD)6Cl2 (Herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers E < 0.8 meV (~J/20). The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wavevectors (1 0 0) and (0 0 3/2), which is consistent with antiferromagnetic correlations between pairs of nearest neighbor Cu impurities on adjacent triangular (Zn) interlay…
Gapless spin liquids on the three dimensional hyper-kagome lattice of Na$_4$Ir$_3$O$_8$
最近的实验表明，Na $_4$ Ir $_3$ O $_8$，其中s=1/2铱局域矩形成角共享三角形的三维网络的材料，可能具有无隙自旋激发的量子自旋液体基态。结合精确对角化、费米平均场基态的对称性分析和Gutzwiller投影变分波函数的研究，我们提出了一种具有自旋费米面的量子自旋液体作为Na $_4$ Ir $_3$ O $_8$超kagome晶格上海森堡模型基态的有利候选.我们提出了这种自旋液体比热的重整化平均场论，并讨论了自旋费米面可能的低温不稳定性。
We study a class of disordered continuous classical spin systems including the kagome Heisenberg magnet. While each term in its local Hamiltonian can be independently minimised, we find {\it discrete} degenerate ground states whose number grows exponentially with system size. These states do not exhibit zero-energy `excitations' characteristic of highly frustrated magnets but instead are local minima of the energy landscape, albeit with an anomalously soft excitation spectrum. This represents a spin liquid version of the phenomenon of jamming familiar from granular media and structural glasses…
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…
Neutron scattering measurements have been performed on deuterated powder samples of claringbullite and Zn-doped claringbullite (Zn$_x$Cu$_{4-x}$(OD)$_{6}$FCl). At low temperatures, claringbullite Cu$_4$(OD)$_{6}$FCl forms a distorted pyrochlore lattice with long-range magnetic order and spin-wave-like magnetic excitations. Partial Zn doping leads to the nominal ZnCu$_3$(OD)$_{6}$FCl compound, a geometrically frustrated spin-1/2 kagome antiferromagnet that shows no transition to magnetic order down to 1.5 K. The magnetic excitations form a gapless continuum, a signature of fractional excitation…
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 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…
Employing large-scale quantum Monte Carlo simulations, we study the extended $XXZ$ model on the kagome lattice. A $\mathbb Z_2$ quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid and ferromagnet. This $\mathbb{Z}_2$ spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the …
We study the ground state phase diagram of a two-dimensional kagome lattice spin-1/2 XY model (J) with a four-site ring exchange interaction (K) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ring exchange, undergoes a direct transition to a Z_2 quantum spin liquid phase at (K/J)_c ~ 22, which is related to the phase proposed by Balents, Girvin and Fisher [Phys. Rev. B, 65 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents z and νfalling in the 3D XY universality class, making it…
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…
We present measurements on a series of materials, Li$_2$In$_{1-x}$Sc$_x$Mo$_3$O$_8$, that can be described as a 1/6th-filled breathing kagome lattice. Substituting Sc for In generates chemical pressure which alters the breathing parameter non-monotonically. $μ$SR experiments show that this chemical pressure tunes the system from antiferromagnetic long range order to a quantum spin liquid phase. A strong correlation with the breathing parameter implies that it is the dominant parameter controlling the level of magnetic frustration, with increased kagome symmetry generating the quantum spin liqu…
The spin-1/2 kagomé Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which unfortunately suffers from the notorious orphan spins problem caused by magnetic disorders. Here we turn to YCu$_3$(OH)$_{6.5}$Br$_{2.5}$, recently recognized as another host of a globally undistorted kagomé Cu$^{2+}$ lattice free from the orphan spins, thus a more feasible system for studying the int…
