arXiv subjects

Xiaoqun Wang

Publications and source records attributed to Xiaoqun Wang.

At least 73 records · Page 4Linked to original sources

arXiv2022

On the error rate of importance sampling with randomized quasi-Monte Carlo

Importance sampling (IS) is valuable in reducing the variance of Monte Carlo sampling for many areas, including finance, rare event simulation, and Bayesian inference. It is natural and obvious to combine quasi-Monte Carlo (QMC) methods with IS to achieve a faster rate of convergence. However, a naive replacement of Monte Carlo with QMC may not work well. This paper investigates the convergence rates of randomized QMC-based IS for estimating integrals with respect to a Gaussian measure, in which the IS measure is a Gaussian or $t$ distribution. We prove that if the target function satisfies the so-called boundary growth condition and the covariance matrix of the IS density has eigenvalues no smaller than 1, then randomized QMC with the Gaussian proposal has a root mean squared error of $O(N^{-1+ε})$ for arbitrarily small $ε>0$. Similar results of $t$ distribution as the proposal are also established. These sufficient conditions help to assess the effectiveness of IS in QMC. For some particular applications, we find that the Laplace IS, a very general approach to approximate the target function by a quadratic Taylor approximation around its mode, has eigenvalues smaller than 1, making the resulting integrand less favorable for QMC. From this point of view, when using Gaussian distributions as the IS proposal, a change of measure via Laplace IS may transform a favorable integrand into unfavorable one for QMC although the variance of Monte Carlo sampling is reduced. We also give some examples to verify our propositions and warn against naive replacement of MC with QMC under IS proposals. Numerical results suggest that using Laplace IS with $t$ distributions is more robust than that with Gaussian distributions.

math.NA↗

arXiv2022

Quantum phase transition in magnetic nanographenes on a lead superconductor

Quantum spins, referred to the spin operator preserved by full SU(2) symmetry in the absence of the magnetic anistropy, have been proposed to host exotic interactions with superconductivity4. However, spin orbit coupling and crystal field splitting normally cause a significant magnetic anisotropy for d/f-shell spins on surfaces6,9, breaking SU(2) symmetry and fabricating the spins with Ising properties10. Recently, magnetic nanographenes have been proven to host intrinsic quantum magnetism due to their negligible spin orbital coupling and crystal field splitting. Here, we fabricate three atomically precise nanographenes with the same magnetic ground state of spin S=1/2 on Pb(111) through engineering sublattice imbalance in graphene honeycomb lattice. Scanning tunneling spectroscopy reveals the coexistence of magnetic bound states and Kondo screening in such hybridized system. Through engineering the magnetic exchange strength between the unpaired spin in nanographenes and cooper pairs, quantum phase transition from the singlet to the doublet state has been observed, in consistent with quantum models of spins on superconductors. Our work demonstrates delocalized graphene magnetism host highly tunable magnetic bound states with cooper pairs, which can be further developed to study the Majorana bound states and other rich quantum physics of low-dimensional quantum spins on superconductors.

cond-mat.mes-hall↗

arXiv2022

Unique quantum impurity states driven by a vortex in topological superconductors

The interplay of magnetic impurity and vortex in a topological superconductor is of fundamental interest with major implications for implementing quantum computation. There are multiple degrees of freedom interacting with the impurity in the system, including the Majorana zero mode (MZM), the Caroli de Gennes Matricon (CdGM) states, and the electron bulk states that form Cooper pairs, which makes the impurity pinned vortex state elusive to date in topological superconductors. Here, we present an accurate solution of the problem, based on a generalized mapping scheme and the density-matrix renormalization group (DMRG) method. We identify in-gap states that are distinct from the established Yu-Shiba-Rusinov (YSR) states. The newly found in-gap physics is driven by three prominent mechanisms: (i) the coupling of impurity and bulk states leading to competition between Kondo screening and Cooper pairing, resulting in a singlet-doublet quantum phase transition, (ii) the coupling of impurity and CdGM states introducing an effective Zeeman splitting to the doublet state, and (iii) the coupling of impurity and MZM turning the singlet-doublet transition into a crossover. These mechanisms cooperatively produce a unique spin-resolved local density of states. Despite the MZM, a robust nearly zero-energy peak is generated, with comparable height but opposite spin polarization as that of the MZM. These results signify novel emergent physics and offer insights to elucidate intriguing experimental phenomena.

cond-mat.supr-con↗

arXiv2022

Catalytic growth of ultralong graphene nanoribbons on insulating substrates

Graphene nanoribbons (GNRs) with widths of a few nanometres are promising candidates for future nano-electronic applications due to their structurally tunable bandgaps, ultrahigh carrier mobilities, and exceptional stability. However, the direct growth of micrometre-long GNRs on insulating substrates, which is essential for the fabrication of nano-electronic devices, remains an immense challenge. Here, we report the epitaxial growth of GNRs on an insulating hexagonal boron nitride (h-BN) substrate through nanoparticle-catalysed chemical vapor deposition (CVD). Ultra-narrow GNRs with lengths of up to 10 μm are synthesized. Remarkably, the as-grown GNRs are crystallographically aligned with the h-BN substrate, forming one-dimensional (1D) moiré superlattices. Scanning tunnelling microscopy reveals an average width of 2 nm and a typical bandgap of ~1 eV for similar GNRs grown on conducting graphite substrates. Fully atomistic computational simulations support the experimental results and reveal a competition between the formation of GNRs and carbon nanotubes (CNTs) during the nucleation stage, and van der Waals sliding of the GNRs on the h-BN substrate throughout the growth stage. Our study provides a scalable, single-step method for growing micrometre-long narrow GNRs on insulating substrates, thus opening a route to explore the performance of high-quality GNR devices and the fundamental physics of 1D moiré superlattices.

cond-mat.mes-hall↗

arXiv2022

Quasi-Monte Carlo-Based Conditional Malliavin Method for Continuous-Time Asian Option Greeks

Although many methods for computing the Greeks of discrete-time Asian options are proposed, few methods to calculate the Greeks of continuous-time Asian options are known. In this paper, we develop an integration by parts formula in the multi-dimensional Malliavin calculus, and apply it to obtain the Greeks formulae for continuous-time Asian options in the multi-asset situation. We combine the Malliavin method with the quasi-Monte Carlo method to calculate the Greeks in simulation. We discuss the asymptotic convergence of simulation estimates for the continuous-time Asian option Greeks obtained by Malliavin derivatives. We propose to use the conditional quasi-Monte Carlo method to smooth Malliavin Greeks, and show that the calculation of conditional expectations analytically is viable for many types of Asian options. We prove that the new estimates for Greeks have good smoothness. For binary Asian options, Asian call options and up-and-out Asian call options, for instance, our estimates are infinitely times differentiable. We take the gradient principal component analysis method as a dimension reduction technique in simulation. Numerical experiments demonstrate the large efficiency improvement of the proposed method, especially for Asian options with discontinuous payoff functions.

math.NA↗

arXiv2021

Unbiased MLMC-based variational Bayes for likelihood-free inference

Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper, we propose several unbiased estimators based on multilevel Monte Carlo (MLMC) for the gradient of Kullback-Leibler divergence between the posterior distribution and the variational distribution when the likelihood is intractable, but can be estimated unbiasedly. The new VB algorithm differs from the VB algorithms in the literature which usually render biased gradient estimators. Moreover, we incorporate randomized quasi-Monte Carlo (RQMC) sampling within the MLMC-based gradient estimators, which was known to provide a favorable rate of convergence in numerical integration. Theoretical guarantees for RQMC are provided in this new setting. Numerical experiments show that using RQMC in MLMC greatly speeds up the VB algorithm, and finds a better parameter value than some existing competitors do.

math.NA↗

arXiv2021

Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na2Co2TeO6

Spin-orbit coupled honeycomb magnets with the Kitaev interaction have received a lot of attention due to their potential of hosting exotic quantum states including quantum spin liquids. Thus far, the most studied Kitaev systems are 4d/5d-based honeycomb magnets. Recent theoretical studies predicted that 3d-based honeycomb magnets, including Na2Co2TeO6 (NCTO), could also be a potential Kitaev system. Here, we have used a combination of heat capacity, magnetization, electron spin resonance measurements alongside inelastic neutron scattering (INS) to study NCTO's quantum magnetism, and we have found a field-induced spin disordered state in an applied magnetic field range of 7.5 T < B (vertical to b-axis) < 10.5 T. The INS spectra were also simulated to tentatively extract the exchange interactions. As a 3d-magnet with a field-induced disordered state on an effective spin-1/2 honeycomb lattice, NCTO expands the Kitaev model to 3d compounds, promoting further interests on the spin-orbital effect in quantum magnets.

cond-mat.str-el↗

arXiv2021

Unveiling the phase diagram of a bond-alternating spin-$\frac12$ $K$-$Γ$ chain

The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev ($K$) interaction and a symmetric off-diagonal $Γ$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$1/2$ $g_x$-$g_y$ $K$-$Γ$ chain by density-matrix renormalization group method where $g_x$ and $g_y$ are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane ($g_x > g_y$) and odd-Haldane ($g_x < g_y$) phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped $A_x$ and $A_y$ phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a six-fold degenerate FM$_{U_6}$ phase where all the spins are parallel to one of the $\pm \hat{x}$, $\pm \hat{y}$, and $\pm \hat{z}$ axes in a six-site spin rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-2 spin-nematic ordering in the latter is also discussed.

cond-mat.str-el↗

arXiv2021

Generic Spiral Spin Liquids

Spiral spin liquids are unique classical spin liquids that occur in many frustrated spin systems, but do not comprise a new phase of matter. Owing to extensive classical ground-state degeneracy, the spins in a spiral spin liquid thermally fluctuate cooperatively from a collection of spiral configurations at low temperatures. These spiral propagation wavevectors form a continuous manifold in reciprocal space, \textit{i.e.}, a spiral contour or a spiral surface, that strongly governs the low-temperature thermal fluctuations and magnetic physics. In this paper, the relevant spin models conveying the spiral spin liquid physics are systematically explored and the geometric origin of the spiral manifold is clarified in the model construction. The spiral spin liquids based on the dimension and the codimension of the spiral manifold are further clarified. For each class, the physical properties are studied both generally and for specific examples. The results are relevant to a wide range of frustrated magnets. A survey of materials is given and future experiments are suggested.

cond-mat.str-el↗

arXiv2021

Gapless quantum spin liquid in a honeycomb $Γ$ magnet

A family of spin-orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal $Γ$ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these systems. However, the ground state of honeycomb $Γ$ model remains elusive, with a suggested zigzag magnetic order. Here we attempt to resolve the puzzle by perturbing the $Γ$ region with a staggered Heisenberg interaction which favours the zigzag ordering. Despite such favour, we find a wide disordered region inclusive of the $Γ$ limit in the phase diagram. Further, this phase exhibits a vanishing energy gap, a collapse of excitation spectrum, and a logarithmic entanglement entropy scaling on long cylinders, indicating a gapless QSL. Other quantities such as plaquette-plaquette correlation are also discussed.

cond-mat.str-el↗

arXiv2021

Effective Model for Rare-earth Kitaev Materials and its Classical Monte Carlo Simulation

Recently, the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid (KSL). In the present work, we firstly propose an effective spin Hamiltonian consistents with the symmetry group of the crystal structure. Then we apply classical Monte Carlo simulations to preliminarily study the model and establish a phase diagram. When approaching to the low temperature limit, several magnetic long range orders are observed, including the stripe, the zigzag, the antiferromagnetic (AFM), the ferromagnetic (FM), the incommensurate spiral (IS), the Multi-$\pmb {Q}$ and the 120°. We further calculate the thermodynamic properties of the system, such as the temperature dependence of the magnetic susceptibility and the heat capacity. The ordering transition temperatures reflected in the two quantities agree with each other. For most interaction regions, the system is magnetically more susceptible in the $ab$-plane than in the $c$-direction. The stripe phase is special, where the susceptibility is fairly isotropic in the whole temperature region. These features provide useful information to understand the magnetic properties of related materials.

cond-mat.str-el↗

arXiv2020

Electron quasi-itinerancy intertwined with quantum order by disorder in pyrochlore iridate magnetism

We point out the emergence of magnetism from the interplay of electron quasi-itinerancy and quantum order by disorder in pyrochlore iridates. Like other Mott insulating iridates, the Ir$^{4+}$ ion in pyrochlore iridates develops an effective ${J=1/2}$ moment from the on-site spin-orbit coupling. We consider the generic symmetry-allowed exchange between these local moments on a pyrochlore lattice and obtain the mean-field phase diagram. Assuming the superexchange is mediated by direct and/or indirect electron hopping via intermediate oxygens, we derive the exchange interactions in the strong coupling regime from the Hubbard model. This exchange has a degenerate classical ground state manifold and quantum fluctuation selects a non-coplanar ground state, known as quantum order by disorder. Extending to the intermediate coupling regime, the same non-coplanar order is selected from the degenerate manifold by the kinetic energy, which is dubbed "electron quasi-itinerancy". We discuss the experimental relevance of our results and electron quasi-itinerancy among other iridates and $4d/5d$ magnets.

cond-mat.str-el↗

arXiv2020

Efficient risk estimation via nested multilevel quasi-Monte Carlo simulation

We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may resort to nested simulation. To reduce the complexity of nested simulation, we present a method that combines multilevel Monte Carlo (MLMC) and quasi-Monte Carlo (QMC). In the outer simulation, we use Monte Carlo to generate financial scenarios. In the inner simulation, we use QMC to estimate the portfolio loss in each scenario. We prove that using QMC can accelerate the convergence rates in both the crude nested simulation and the multilevel nested simulation. Under certain conditions, the complexity of MLMC can be reduced to $O(ε^{-2}(\log ε)^2)$ by incorporating QMC. On the other hand, we find that MLMC encounters catastrophic coupling problem due to the existence of indicator functions. To remedy this, we propose a smoothed MLMC method which uses logistic sigmoid functions to approximate indicator functions. Numerical results show that the optimal complexity $O(ε^{-2})$ is almost attained when using QMC methods in both MLMC and smoothed MLMC, even in moderate high dimensions.

math.NA↗

arXiv2020

Designer spin order in diradical nanographenes

The magnetic properties of carbon materials are at present the focus of an intense research effort in physics, chemistry and materials science due to their potential applications in spintronics and quantum computations. Although the presence of spins in open-shell nanographenes has been recently confirmed, the ability to control magnetic coupling sign has remained elusive, but the most desirable. Here, we demonstrate an effective approach of engineering magnetic ground states in atomically precise open-shell bipartite/nonbipartite nanographenes using combined scanning probe techniques and mean-field Hubbard model calculations. The magnetic coupling sign between two spins has been controlled via breaking bipartite lattice symmetry of nanographenes. In addition, the exchange-interaction strength between two spins has been widely tuned by finely tailoring their spin density overlap, realizing a large exchange-interaction strength of 42 meV. Our demonstrated method provides ample opportunities for designer above-room-temperature magnetic phases and functionalities in graphene nanomaterials.

cond-mat.mes-hall↗

arXiv2020

Effective Magnetic Hamiltonian at Finite Temperatures for Rare Earth Chalcogenides

Alkali metal rare-earth chalcogenide $ARECh2$ (A=alkali or monovalent metal, RE=rare earth, Ch=O, S, Se, Te), is a large family of quantum spin liquid (QSL) candidates we discovered recently. Unlike $YbMgGaO4$, most members in the family except for the oxide ones, have relatively small crystalline electric-field (CEF) excitation levels, particularly the first ones. This makes the conventional Curie-Weiss analysis at finite temperatures inapplicable and CEF excitations may play an essential role in understanding the low-energy spin physics. Here we considered an effective magnetic Hamiltonian incorporating CEF excitations and spin-spin interactions, to accurately describe thermodynamics in such a system. By taking $NaYbSe2$ as an example, we were able to analyze magnetic susceptibility, magnetization under pulsed high fields and heat capacity in a systematic and comprehensive way. The analysis allows us to produce accurate anisotropic exchange coupling energies and unambiguously determine a crossover temperature ($\sim$25 K in the case of $NaYbSe2$), below which CEF effects fade away and pure spin-spin interactions stand out. We further validated the effective picture by successfully explaining the anomalous temperature dependence of electron spin resonance (ESR) spectral width. The effective scenario in principle can be generalized to other rare-earth spin systems with small CEF excitations.

cond-mat.str-el↗

arXiv2020

Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO$_4$

We propose quenched disorders could bring novel quantum excitations and models to certain quantum magnets. Motivated by the recent experiments on the quantum Ising magnet TmMgGaO$_4$, we explore the effects of the quenched disorder and the interlayer coupling in this triangular lattice Ising antiferromagnet. It is pointed out that the weak quenched (non-magnetic) disorder would convert the emergent 2D Berezinskii-Kosterlitz-Thouless (BKT) phase and the critical region into a gauge glass. There will be an emergent Halperin-Saslow mode associated with this gauge glass. Using the Imry-Ma argument, we further explain the fate of the finite-field $C_3$ symmetry breaking transition at the low temperatures. The ferromagnetic interlayer coupling would suppress the BKT phase and generate a tiny ferromagnetism. With the quenched disorders, this interlayer coupling changes the 2D gauge glass into a 3D gauge glass, and the Halperin-Saslow mode persists. This work merely focuses on addressing a phase regime in terms of emergent U(1) gauge glass behaviors and hope to inspire future works and thoughts in weakly disordered frustrated magnets in general.

cond-mat.str-el↗

arXiv2020

Clusterization transition between cluster Mott insulators on a breathing Kagomé lattice

Motivated by recent experimental progress on various cluster Mott insulators, we study an extended Hubbard model on a breathing Kagomé lattice with a single electron orbital and $1/6$ electron filling. Two distinct types of cluster localization are found in the cluster Mott regime due to the presence of the electron repulsion between neighboring sites, rather than from the on-site Hubbard interaction in the conventional Mott insulators. We introduce a unified parton construction framework to accommodate both type of cluster Mott insulating phase as well as a trivial Ferm liquid metal and discuss the phase transitions in the phase diagram. It is shown that, in one of the cluster localization phases, the strong inter-site repulsion results into locally metallic behavior within one of two triangular clusters on the breathing Kagomé lattice. We further comment on experimental relevance to existing Mo-based cluster magnets.

cond-mat.str-el↗

arXiv2020

Multinode quantum spin liquids on the honeycomb lattice

Recently it was realized that the zigzag magnetic order in Kitaev materials can be stabilized by small negative off-diagonal interactions called the $Γ'$ terms. To fully understand the effect of the $Γ'$ interactions, we investigate the quantum $K$-$Γ$-$Γ'$ model on the honeycomb lattice using the variational Monte Carlo method. Two multinode Z$_2$ quantum spin liquids (QSLs) are found at $Γ'>0$, one of which is the previously found proximate Kitaev spin liquid called the PKSL14 state which shares the same projective symmetry group (PSG) with the Kitaev spin liquid. A remarkable result is that a $π$-flux state with a distinct PSG appears at larger $Γ'$. The $π$-flux state is characterized by an enhanced periodic structure in the spinon dispersion in the original Brillouin zone (BZ), which is experimentally observable. Interestingly, two PKSL8 states are competing with the $π$-flux state and one of them can be stabilized by six-spin ring-exchange interactions. The physical properties of these nodal QSLs are studied by applying magnetic fields and the results depend on the number of cones. Our study infers that there exist a family of zero-flux QSLs that contain $6n+2, n\in\mathbb Z$ Majorana cones and a family of $π$-flux QSLs containing $4(6n+2)$ cones in the original BZ. It provides guidelines for experimental realization of non-Kitaev QSLs in relevant materials.

cond-mat.str-el↗