We present a large-N variational approach to describe the magnetism of insulating doped semiconductors based on a disorder-generalization of the resonating-valence-bond theory for quantum antiferromagnets. This method captures all the qualitative and even quantitative predictions of the strong-disorder renormalization group approach over the entire experimentally relevant temperature range. Finally, by mapping the problem on a hard-sphere fluid, we could provide an essentially exact analytic solution without any adjustable parameters.
Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$
我们推广了Sandvik、Beach和Evertz（A. W. Sandvik，Phys. Rev. 95，207203（2005）; K. S. D.海滩和A. W. Sandvik，Nucl.Phys.B750，142（2006）; A. W. Sandvik和H. G. Evertz，arXiv：0807.0682，unpublished.）反铁磁哈密顿量的基态在有限尺寸系统中具有总自旋$S_{tot} = 1/2$的情况。我们解释了各种基态的期望值可以通过在单重态的情况下开发的估计的泛化计算，并说明了该方法的功率通过计算基态的自旋纹理和键能在一个$L \times L$海森堡反铁磁体与$L$奇数和自由边界。
The Néel temperature, staggered magnetization density, as well as the spinwave velocity of a three-dimensional (3D) quantum Heisenberg model with antiferromagnetic disorder (randomness) are calculated using first principles non-perturbative quantum Monte Carlo simulations. In particular, we examine the validity of universal scaling relations that are related to these three studied physical quantities. These relations are relevant to experimental data and are firmly established for clean (regular) 3D dimerized spin-1/2 Heisenberg models. Remarkably, our numerical results show that the considere…
A molecular Mott insulator $κ$-(ET)$_2$B(CN)$_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits a quantum disordered state with gapped spin excitation in the ground state. $^{13}$C nuclear magnetic resonance, magnetization, and magnetic torque measurements reveal that magnetic field suppresses valence bond order and induces long-range magnetic order above a critical field $\sim 8$ T. The nuclear spin-lattice relaxation rate $1/T_1$ shows persistent evolution of antiferromagnetic correlation above the transition temperature, highlighting a quantum spin…
We use exact quantum Monte Carlo simulations to demonstrate that the Néel ground state of an antiferromagnetic SU(2) spin-$\frac{1}{2}$ Heisenberg model on the honeycomb lattice can be destroyed by a coupling to quantum phonons. We find a clear first-order transition to a valence-bond-solid state with Kekulé order instead of a deconfined quantum critical point. However, quantum lattice fluctuations can drive the transition towards weakly first-order, revealing a tunability of the transition by the retardation of the interaction. In contrast to the one-dimensional case, our phase diagram in the…
We present numerical evidence for the emergence of an extended valence bond solid (VBS) phase at $T=0$ in the kagome $S=1/2$ Heisenberg antiferromagnet with ferromagnetic further-neighbor interactions. The VBS is located at the boundary between two magnetically ordered regions and extends close to the nearest-neighbor Heisenberg point. It exhibits a diamond-like singlet covering pattern with a $12$-site unit-cell. Our results suggest the possibility of a direct, possibly continuous, quantum phase transition from the neighboring $\mathbf{q}=0$ coplanar magnetically ordered phase into the VBS ph…
We use a strong-disorder renormalization group (SDRG) method and ground-state quantum Monte Carlo (QMC) simulations to study S=1/2 spin chains with random couplings, calculating disorder-averaged spin and dimer correlations. The QMC simulations demonstrate logarithmic corrections to the power-law decaying correlations obtained with the SDRG scheme. The same asymptotic forms apply both for systems with standard Heisenberg exchange and for certain multi-spin couplings leading to spontaneous dimerization in the clean system. We show that the logarithmic corrections arise in the valence-bond (sing…
We study the evolution of magnetic excitations in the disordered two-dimensional antiferromagnet Sr2Ir1-xRuxO4. A gigantic magnetic gap greater than 40 meV opens at x = 0.27 and increases with Ru concentration, rendering the dispersive magnetic excitations in Sr2IrO4 almost momentum independent. Up to a Ru concentration of x = 0.77, both experiments and first-principles calculations show the Ir Jeff = 1/2 state remains intact. The magnetic gap arises from the local interaction anisotropy in the proximity of the Ru disorder. Under the coherent potential approximation, we reproduce the experimen…
Using the infinite Projected Entangled Pair States (iPEPS) algorithm, we study the ground-state properties of the spin-$1/2$ quantum Heisenberg antiferromagnet on the star lattice in the thermodynamic limit. By analyzing the ground-state energy of the two inequivalent bonds of the lattice in different unit-cell structures, we identify two competing Valence-Bond-Solid (VBS) phases for different antiferromagnetic Heisenberg exchange couplings. More precisely, we observe (i) a VBS state which respects the full symmetries of the Hamiltonian, and (ii) a resonating VBS state which, in contrast to pr…
The two-dimensional Su-Schrieffer-Heeger model of electrons coupled to quantum phonons is investigated using Langevin dynamics within the framework of auxiliary-field quantum Monte Carlo. Based on an explicit determination of the density of zeros of the fermion determinant, it is argued that the method is efficient in the challenging adiabatic limit. Large-scale simulations at the O(4)-symmetric point establish that the ground state of the 2D SSH model undergoes a transition from a $(π,π)$ valence bond solid to an antiferromagnet with increasing phonon frequency, yet still in the adiabatic reg…
Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
Valence bond crystal in a pyrochlore antiferromagnet with orbital degeneracy
本文讨论了三重轨道简并$S=1/2$磁性离子的烧绿石晶格的基态。我们推导出一个有效的自旋轨道哈密顿量，并表明轨道自由度可以调制自旋交换，消除无限自旋简并烧绿石结构的特点。由此产生的状态是自旋单重态二聚体的集合，由于它们的相对取向而具有残余简并性。后者被磁弹性相互作用提升，在自旋单态相空间中诱导，迫使四重态畸变。这种理论为在B-尖晶石MgTi $_2$ O $_4$中观察到的螺旋自旋单态模式提供了解释。
