We investigate LiVS2 and LiVSe2 with a triangular lattice as itinerant analogues of LiVO2, known for the formation of valence bond solid (VBS) state out of S = 1 frustrated magnet. LiVS2, which is located at the border between a metal and a correlated insulator, shows a first ordered transition from a paramagnetic metal to a VBS insulator at Tc ~ 305 K upon cooling. The presence of VBS state in the close vicinity of insulator-metal transition may suggest the importance of itinerancy in the formation of VBS state. We argue that the high temperature metallic phase of LiVS2 has a pseudo-gap, likely originating from the VBS fluctuation. LiVSe2 was found to be a paramagnetic metal down to 2 K.
We present a real-space view of one-dimensional (1D) to three-dimensional (3D) topological materials with 13 representative samples selected from each class, including 1D trans-polyacetylene, two-dimensional (2D) graphene, and 3D topological insulators, Dirac semimetals, Weyl semimetals, and nodal-line semimetals. This review is not intended to present a complete up-to-date list of publications on topological materials, nor to provide a progress report on the theoretical concepts and experimental advances, but rather to focus on an analysis based on the valence-bond model to help the readers g…
Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8
从简单的成分中出现复杂的电子行为导致了许多物质状态的发现。在表现出几何磁阻挫的系统中发现了许多例子，这阻止了所有磁相互作用的同时满足。这种挫折产生了复杂的磁性，如手性自旋结构轨道驱动的磁性，自旋冰行为表现出狄拉克弦与磁单极，价键固体和自旋液体。在这里，我们报告的合成和表征LiZn 2 Mo 3 O 8，几何阻挫反铁磁体中的磁矩是本地化的小过渡金属簇，而不是个别离子。通过这样做，一阶Jahn-Teller不稳定性和轨道排序被阻止，允许在LiZn 2 Mo 3 O 8中的强相互作用的磁性团簇可能引起一个奇特的凝聚价键基态，让人想起所提出的共振价键态。我们的研究结果还将集群上的磁性与扩展固体中的几何磁性挫折联系起来，展示了一种新的方法，可以在寻找集体，紧急电子状态的物质时实现无与伦比的化学控制和可调性。
$Li_{2}RuO_{3}$ with a honeycomb structure undergoes a drastic transition from a regular honeycomb lattice with the $C2/m$ space group to a valence bond solid state of the $P2_{1}/m$ space group with an extremely strong dimerization at 550 K. We synthesized $Li_{2}Ru_{1-x}Mn_{x}O_{3}$ with a full solid solution and investigated doping effects on the valence bond solid state as a function of Mn content. The valence bond solid state is found to be stable up to $x = 0.2$, based on our extensive experiments: structural studies, resistivity, and magnetic susceptibility. On the other hand, the exten…
The hardcore extended Bose Hubbard model on a bilayer square lattice with attractive (repulsive) interplane (intraplane) interactions has been investigated numerically. Focusing on the strong interplane hopping parameter regime, triplet valence bonds of dimers are stabilized to form valence bond checkerboard solid at quarter filling. Increasing the particle number we confirm, for the first time, the presence of the exotic valence bond supersolid phase, where the valence bond solid ordering and the boson superfluidity coexist. Rising further the particle number will lead to a checkerboard solid…
Short-range resonating-valence bond states in an orbitally degenerate magnet on a honeycomb lattice is studied. A quantum-dimer model is derived from the Hamiltonian which represents the superexchange interaction and the dynamical Jahn-Teller (JT) effect. We introduce two local units termed "spin-orbital singlet dimer", where two spins in a nearest-neighbor bond form a singlet state associated with an orbital polarization along the bond, and "local JT singlet", where an orbital polarization is quenched due to the dynamical JT effect. A derived quantum-dimer model consists of the hopping of the…
Doped IrTe$_2$ is considered a platform for topological superconductivity and therefore receives currently a lot of interest. In addition, the superconductivity in these materials exists in close vicinity of electronic valence bond crystals, which we explore here by means of high-pressure single crystal x-ray diffraction in combination with density functional theory. Our crystallographic refinements provide unprecedented information about the structural evolution as a function of applied pressure up to 42 GPa. Using this structural information for density functional theory calculations, we sho…
We show that the mean-field resonating valence bond approximation proposed in 1987 by Baskaran, Zou, and Anderson describes gapless charge pair excitations confined to the boundaries of the spinon Brillouin zone. The existence of such pairs accounts for all the essential anomalous electronic properties of cuprates, with superconductivity arising due to the charge drag by the spinon superflow. This mechanism may be relevant to other unconventional superconductors.
We develop a quantum spin liquid theory for quantum magnets with easy-plane ferromagnetic exchange. These strongly entangled quantum states are obtained by dimer coverings of 2D lattices with triplet $S = 1, m_z = 0$ bonds, forming a triplet resonating valence bond (tRVB) state. We discuss the conditions and the procedure to transfer well-known results from conventional singlet resonating valence bond theory to tRVB. Additionally, we present mean field theories of Abrikosov fermions on 2D triangular and square lattices, which can be controlled in an appropriate large $N$ limit. We also incorpo…
Recent evidence from magnetic torque, electron spin resonance, and second harmonic generation indicate that the prototypical quantum spin liquid candidate, herbertsmithite, has a symmetry lower than its x-ray refined trigonal space group. Here, we consider known and possible distortions of this mineral class, along with related copper kagome oxides and fluorides, relate these to possible valence bond patterns, and comment on their relevance to the physics of these interesting materials.
Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.
On the basis of a Berry-phase analysis, we study the ground state of the $J_1$-$J_2$ Heisenberg chain for $S=2,3,4$. We find that changes of the Berry phase occur $S$ times for spin-$S$ systems, indicating the sequential phase transitions. The sequential phase transitions are associated with the change of valence-bond configurations of the ground states. To demonstrate this numerically, we connect the $J_1$-$J_2$ Heisenberg Hamiltonian with the generalized Affleck-Kennedy-Lieb-Tasaki model, and show that the different phases are connected to the different valence-bond-solid states.
A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a quantum spin system where local spin singlets are formed in some regular pattern. We here study the competition between VBS order and a fully polarized ferromagnetic state as function of an external magnetic field in a one-dimensional extended Heisenberg model---the J-Q$_2$ model---using stochastic series expansion quantum Monte Carlo simulations with directed loop updates. We discuss the ground state phase diagram.
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. C…
Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids (QSL). Here, we show that excitations related to singlet breaking on nearest-neighbor bonds describe the high-energy part of the excitation spectrum in YbMgGaO4, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering (INS) study, we demonstrate that nearest-neighbor RVB excitations account fo…
We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with $C_{4v}$ point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular $S$ and $T$ matrices by constructing all nine topological sectors on a torus and establish the existence of $\mathbb{Z}_3$ topological order in this SU(3) tRVB state.
