Based on the self-consistent T-matrix approximation (SCTMA), analytical theory of density of states (DOS) in three-dimensional quantum magnets with the bond disorder is proposed. It successfully describes DOS in both cases of resonant and non-resonant scattering which appearance is governed by the ratio of scattering length and the average distance between impurities. Corrections to the quasiparticles band gap in these cases are shown to be $\propto c^{2/3}$ and $\propto c$, respectively. Moreover, the theory yields a semi-circle form of DOS for the bound states inside the gap which results in highly nontrivial DOS in the intermediate parameters region between two limiting cases when the band DOS and the semi-circle are overlapped. Long-wavelength excitations are discussed. In the resonant regime their damping is almost constant $\propto c^{2/3}$, which according to Ioffe-Regel criterion means their localization. Applicability of the theory is illustrated by a quantitative description of the recent experimental data on spin-dimer system Ba$_{3-x}$Sr$_x$Cr$_2$O$_8$.
We present the results of finite-temperature classical Monte Carlo simulations of a strongly spin-orbit-coupled nearest-neighbor triangular-lattice model for the candidate $\mathrm{U}(1)$ quantum spin liquid $\mathrm{YbMgGaO}_4$ at large system sizes. We find a single continuous finite-temperature stripe-ordering transition with slowly diverging heat capacity that completely breaks the sixfold ground-state degeneracy, despite the absence of a known conformal field theory describing such a transition. We also simulate the effect of random-bond disorder in the model, and find that even weak bond…
We study effects of quenched bond disorder in frustrated easy-plane antiferromagnets in two space dimensions, using a combination of analytical and numerical techniques. We consider local-moment systems which display non-collinear long-range order at zero temperature, with the antiferromagnetic triangular-lattice XY model as a prime example. We show that (i) weak bond disorder transforms the clean ground state into a state with quasi-long-range order, and (ii) strong bond disorder results in a short-range-ordered glassy ground state. Using extensive Monte Carlo simulations, we also track the f…
用随机级数展开量子蒙特卡罗方法研究了反铁磁自旋1/2海森堡阶梯中的随机键无序。我们发现，个别键杂质的影响有很大的不同，这取决于他们的位置腿和梯级。我们首先集中在如何分布的局部键能依赖于杂质浓度。然后我们研究了无规键掺杂对偶脚梯形相图的影响。我们观察到玻色玻璃相在两个制度（$h' < h \lesssim h_{c1}$和$h" < h <h_{c2}$）和玻色-爱因斯坦凝聚体之间。它们的存在进行了讨论的关系，当地的键能。
Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder
基于阻挫磁性材料中令人困惑的自旋玻璃行为，我们从理论上研究了几何阻挫经典自旋模型中的磁弹性耦合效应。特别是，我们认为键无序海森堡反铁磁体的烧绿石晶格耦合到本地晶格畸变。通过对晶格自由度的积分，我们得到了一个有效的纯自旋模型，即具有键无序的双线性双二次模型，并利用经典的蒙特卡罗模拟对该模型进行了分析。首先，我们讨论了相图以及热力学和磁学性质。我们发现，自旋玻璃转变温度大大提高了自旋-晶格耦合$b$在弱无序制度。这种增强归因于自旋-晶格耦合的存在下形成的半离散简并流形中的热涨落的抑制。我们还发现，随着无序度的增加，在由$b$确定的温度下，体系表现出与键无序度无关的自旋玻璃态和有序度的伴随转变.虽然进一步的邻居交换相互作用起源于合作晶格扭曲的结果在弱无序制度的自旋晶格顺序，伴随的过渡仍然是强大的。我们通过分析磁化率、非线性磁化率和比热的磁滞现象来研究伴随跃迁的性质。此外，我们还讨论了高温顺磁相的线性和非线性磁化率以及顺磁相的单自旋翻转动力学。所有这些结果进行了讨论，与典型的烧绿石磁铁，如Y2 Mo 2 O 7和ZnCr 2 O 4的实验比较。
The 5d-electron honeycomb compound H$_3$LiIr$_2$O$_3$ [K. Kitagawa $et$ $al.$, Nature 554, 341-345 (2018)] exhibits an apparent quantum spin liquid (QSL) state. In this intercalated spin-orbital compound, a remarkable pile up of low-energy states was experimentally observed in specific heat and nuclear magnetic (NMR) spin relaxation. We show that a bond disordered Kitaev model can naturally account for this phenomenon, suggesting that disorder plays an essential role in its theoretical description. In the exactly soluble Kitaev model, we obtain, via spin fractionalization, a random bipartite h…
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…
By using Lanczos exact diagonalization and quantum Monte Carlo combined with stochastic analytic continuation, we study the dynamical properties of the $S=1$ antiferromagnetic Heisenberg chain with different strengths of bond disorder. In the weak disorder region, we find weakly coupled bonds which can induce additional low-energy excitation below the one-magnon mode. As the disorder increases, the average Haldane gap closes at $δ_Δ\sim 0.5$ with more and more low-energy excitations coming out. After the critical disorder strength $δ_c\sim 1$, the system reaches a random-singlet phase with pro…
We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground state is characterized by non-collinear long-range order with non-zero vector chirality, and study the effects of quenched bond disorder, i.e., random exchange couplings. A single bond defect is known to induce a dipolar texture in the spin background independent of microscopic details. Using general analytical arguments as well as large-scale simulations for the classical triangular-lattice Heisenberg model, we show that any finite concentration of such defects destroys long-range order for spatial dimension $d\leq 2…
Inhomogeneous ordering in weakly coupled Heisenberg $S=1/2$ chains with random bonds
在$μ$ SR实验中研究了准一维无规键反铁磁体BaCu $_2$（Si $_{1-x}$ Ge $_{x}$）$_2$ O $_7$中长程磁有序随无序强度的变化.与无无序母体材料相比，饱和有序矩被发现大大降低。此外，即使在弱无序的物种，磁有序状态被证明是高度不均匀的。结果解释弱耦合随机自旋链，由``无限随机``不动点。
Recent theoretical proposals have argued that cobaltates with edge-sharing octahedral coordination can have significant bond-dependent exchange couplings thus offering a platform in 3$d$ ions for such physics beyond the much-explored realizations in 4$d$ and 5$d$ materials. Here we present high-resolution inelastic neutron scattering data within the magnetically ordered phase of the stacked honeycomb magnet CoTiO$_3$ revealing the presence of a finite energy gap and demonstrate that this implies the presence of bond-dependent anisotropic couplings. We also show through an extensive theoretical…
Structural and spin-glass properties of single crystal $J_{eff}$ = 1/2 pyrochlore antiferromagnet NaCdCo$_2$F$_7$ : correlating $T_f$ with magnetic-bond-disorder
Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
Kitaev在蜂窝格子上的罗盘模型实现了一种自旋液体，它的出射激发是色散的Majorana费米子和静态的Z_2规范通量。基于Pedrocchi，Chesi和Loss最近的一篇论文[Phys. Rev. B 84，165414（2011）]，我们讨论了Majorana表示中有限尺寸模拟的物理状态的适当选择。某些物理观测量获得大的有限尺寸效应，特别是如果基态是不是费米子自由，我们证明一般适用于系统中的无隙阶段和周期性的边界条件。为了说明我们的研究结果，我们计算有限尺寸系统的静态和动态自旋磁化率。具体来说，我们考虑随机键无序（保留了模型的溶解度），计算局部磁通间隙的分布，并提取NMR线形。我们还预测了一个过渡到一个随机通量状态，增加混乱。
We report high-frequency/high-field electron spin resonance (ESR) and high-field magnetization studies on single crystals of the bond-disordered pyrochlore NaCaCo$_2$F$_7$. Frequency- and temperature-dependent ESR investigations above the freezing temperature $T_f \sim 2.4$ K reveal the coexistence of two distinct magnetic phases. A cooperative paramagnetic phase, evidenced by a gapless excitation mode, is found as well as a spin-glass phase developing below 20 K which is associated with a gapped low-energy excitation. Effective $g$-factors close to 2 are obtained for both modes in line with p…
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2d valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with i…
We investigate the growth of the entanglement entropy $S_{\textrm{ent}}$ following global quenches in two-dimensional free fermion models with potential and bond disorder. For the potential disorder case we show that an intermediate weak localization regime exists in which $S_{\textrm{ent}}(t)$ grows logarithmically in time $t$ before Anderson localization sets in. For the case of binary bond disorder near the percolation transition we find additive logarithmic corrections to area and volume laws as well as a scaling at long times which is consistent with an infinite randomness fixed point.
We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using exact diagonalization and the strong disorder renormalization group method, we demonstrate that this approach gives results in agreement with the use of traditional topological invariants, especially in cases where topological order is known to persist in the presence of off-diagonal bond disorder. The entanglement gap is then used to analyze classes of quant…
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d=2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d=2. If one trusts these computations also in d=3, one finds results con…
