Motivated by the recent discovery of the Z_2 quantum spin liquid state in the nearest neighbor Heisenberg model on the kagome lattice, we investigate the "even-odd" effect occuring when this state is confined to infinitely long cylinders of finite circumference. We pursue a dual analysis, where we map the effective Z_2 gauge theory from the kagome lattice to a frustrated Ising model on the dice lattice. Unexpectedly, we find that the latter theory, if restricted to nearest neighbor interactions, is insufficient to capture this effect. We provide an explanation of why further neighbor interactions are needed via a high-temperature expansion of the effective Hamiltonian. We then carry out projective symmetry group analysis to understand which second neighbor interactions can be introduced while respecting the lattice symmetries. Finally, we qualitatively compare our results to numerics by computing the dimerization operator within our theory. Systems with odd circumferences exhibit a non-vanishing dimerization that decays exponentially with circumference.
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 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 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…
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.
Spin-1/2 Heisenberg antiferromanget on kagome: a $Z_2$ spin liquid with fermionic spinons
受最近对kagome上自旋为1/2的海森堡反铁磁体的数值和实验研究的启发，我们建立了一个费米子自旋子的多体模型[Phys. Rev. Lett. 103，187203（2009）]。在S=0通道中，自旋子与突现的U（1）规范场相互作用，并受到强烈的短程吸引。该模型的基态一般为$Z_2$液体。我们计算的边缘的两个自旋连续和比较的理论从费米子方法的海森堡模型。
Instabilities of Spin-Liquid States in a Quantum Kagome Antiferromagnet
由于几何挫折而产生的自旋液体的涌现行为使它们成为一种有趣的物质状态。我们表明，在量子kagome反铁磁体ZnCu $_3$（OH）$_6$ SO $_4$中存在几种不同的相关但波动的状态。通过结合互补的本地探测技术与中子散射，我们发现了一个交叉从临界制度到一个无间隙的自旋液相随着温度的降低。后一相的额外非常规不稳定性导致在最低温度下稳定的第二种不同的自旋液体状态。我们将这种复杂的行为作为不同受抑量子磁体的共同特征。
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…
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。
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…
Tunable quantum spin liquidity in the 1/6th-filled breathing kagome lattice
我们提出了一系列材料，Li $_2$ In $_{1-x}$ Sc $_x$ Mo $_3$ O $_8$，可以被描述为1/6填充呼吸戈薇晶格的测量。用Sc代替In产生化学压力，其非单调地改变呼吸参数。$μ$ SR实验表明，该化学压力将系统从反铁长程序调谐到量子自旋液体相。与呼吸参数的强相关性意味着它是控制磁挫挫水平的主导参数，增加的kagome对称性产生量子自旋液体相。磁化率测量表明，这与晶格对称性变化引起的不同类型的电荷有序有关，符合Chen等人的理论[Phys. Rev. B 93，245134（2016）]。在中等Sc浓度和最小呼吸参数下，样品的比热与预测的$U(1)$量子自旋液体一致。
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…
We have employed a magnetic field angle as a tuning parameter in a comprehensive measurement of the specific heat, magnetocaloric effect, and magnetization for the quasi-kagome Kondo lattice CeRhSn, which is considered to exhibit zero-field quantum criticality driven by geometrical frustration. By constructing the field-angle-resolved landscape of the entropy, we unexpectedly revealed that the non-Fermi-liquid nature survives up to a metamagnetic crossover field of roughly 3 T in the very narrow field-orientation range, close to the direction parallel to the quasi-kagome plane. We propose that…
The spin-$\frac{1}{2}$ kagome antiferromagnet is considered an ideal host for a quantum spin liquid ground state. We find that when the bonds of the kagome lattice are modulated with a periodic pattern, new quantum ground states emerge. Newly synthesized crystalline barlowite (Cu$_4$(OH)$_6$FBr) and Zn-substituted barlowite demonstrate the delicate interplay between singlet states and spin order on the spin-$\frac{1}{2}$ kagome lattice. Comprehensive structural measurements demonstrate that our new variant of barlowite maintains hexagonal symmetry at low temperatures with an arrangement of dis…
