Searcharxiv⌕ Search

arXiv subjects

Xiaoqun Wang

Publications and source records attributed to Xiaoqun Wang.

At least 55 records · Page 3Linked to original sources
arXiv2024

Interacting lattice systems with quantum dissipation: a quantum Monte Carlo study

Quantum dissipation arises when a large system can be split in a quantum system and an environment where the energy of the former flows to. Understanding the effect of dissipation on quantum many-body systems is of particular importance due to its potential relations with quantum information processing. We propose a conceptually simple approach to introduce the dissipation into interacting quantum systems in a thermodynamical context, in which every site of a 1d lattice is coupled off-diagonally to its own bath. The interplay between quantum dissipation and interactions gives rise to counterintuitive interpretations such as a compressible zero-temperature state with spontaneous discrete symmetry breaking and a thermal phase transition in a one-dimensional dissipative quantum many-body system as revealed by Quantum Monte Carlo path integral simulations.

cond-mat.str-el↗
arXiv2024

Thermal Tensor Network Approach for Spin-Lattice Relaxation in Quantum Magnets

Low-dimensional quantum magnets, particularly those with strong spin frustration, are characterized by their notable spin fluctuations. Nuclear magnetic resonance (NMR) serves as a sensitive probe of low-energy fluctuations that offers valuable insight into rich magnetic phases and emergent phenomena in quantum magnets. Although experimentally accessible, the numerical simulation of NMR relaxation rates, specifically the spin-lattice relaxation rate $1/T_1$, remains a significant challenge. Analytical continuation based on Monte Carlo calculations are hampered by the notorious negative sign for frustrated systems, and the real-time simulations incur significant costs to capture low-energy fluctuations. Here we propose computing the relaxation rate using thermal tensor networks (TTNs), which provides a streamlined approach by calculating its imaginary-time proxy. We showcase the accuracy and versatility of our methodology by applying it to one-dimensional spin chains and two-dimensional lattices, where we find that the critical exponents $η$ and $zν$ can be extracted from the low-temperature scalings of the simulated $1/T_1$ near quantum critical points. Our results also provide insights into the low-dimensional and frustrated magnetic materials, elucidating universal scaling behaviors in the Ising chain compound CoNb$_2$O$_6$ and revealing the renormalized classical behaviors in the triangular-lattice antiferromagnet Ba$_8$CoNb$_6$O$_{24}$. We apply the approach to effective model of the family of frustrated magnets AYbCh$_2$ (A = Na, K, Cs, and Ch = O, S, Se), and find dramatic changes from spin ordered to the proposed quantum spin liquid phase. Overall, with high reliability and accuracy, the TTN methodology offers a systematic strategy for studying the intricate dynamics observed across a broad spectrum of quantum magnets and related fields.

cond-mat.str-el↗
arXiv2024

Ultra-Long Homochiral Graphene Nanoribbons Grown Within h-BN Stacks for High-Performance Electronics

Van der Waals encapsulation of two-dimensional materials within hexagonal boron nitride (h-BN) stacks has proven to be a promising way to create ultrahigh-performance electronic devices. However, contemporary approaches for achieving van der Waals encapsulation, which involve artificial layer stacking using mechanical transfer techniques, are difficult to control, prone to contamination, and unscalable. Here, we report on the transfer-free direct growth of high-quality graphene nanoribbons (GNRs) within h-BN stacks. The as-grown embedded GNRs exhibit highly desirable features being ultralong (up to 0.25 mm), ultranarrow ( < 5 nm), and homochiral with zigzag edges. Our atomistic simulations reveal that the mechanism underlying the embedded growth involves ultralow GNR friction when sliding between AA'-stacked h-BN layers. Using the grown structures, we demonstrate the transfer-free fabrication of embedded GNR field-effect devices that exhibit excellent performance at room temperature with mobilities of up to 4,600 $cm^{2} V^{-1} s^{-1}$ and on-off ratios of up to $10^{6}$. This paves the way to the bottom-up fabrication of high-performance electronic devices based on embedded layered materials.

cond-mat.mes-hall↗
arXiv2024

Quasi-Monte Carlo and importance sampling methods for Bayesian inverse problems

Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC with low discrepancy points and has the potential to substantially enhance error rates. In this paper, we integrate IS with a randomly shifted rank-1 lattice rule, a widely used QMC method, to approximate posterior expectations arising from Bayesian Inverse Problems (BIPs) where the posterior density tends to concentrate as the intensity of noise diminishes. Within the framework of weighted Hilbert spaces, we first establish the convergence rate of the lattice rule for a large class of unbounded integrands. This method extends to the analysis of QMC combined with IS in BIPs. Furthermore, we explore the robustness of the IS-based randomly shifted rank-1 lattice rule by determining the quadrature error rate with respect to the noise level. The effects of using Gaussian distributions and $t$-distributions as the proposal distributions on the error rate of QMC are comprehensively investigated. We find that the error rate may deteriorate at low intensity of noise when using improper proposals, such as the prior distribution. To reclaim the effectiveness of QMC, we propose a new IS method such that the lattice rule with $N$ quadrature points achieves an optimal error rate close to $O(N^{-1})$, which is insensitive to the noise level. Numerical experiments are conducted to support the theoretical results.

math.NA↗
arXiv2024

Eigenstate properties of the disordered Bose-Hubbard chain

Many-body localization (MBL) of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half. The von Neumann entanglement entropy SvN is commonly used to detect the MBL phase transition but remains challenging to be directly measured. Based on the U(1) symmetry from the particle number conservation, SvN can be decomposed into the particle number entropy SN and the configuration entropy SC. In light of the tendency that the eigenstate's SC nears zero in the localized phase, we introduce a quantity describing the deviation of SN from the ideal thermalization distribution; finite-size scaling analysis illustrates that it shares the same phase transition point with SvN but displays the better critical exponents. This observation hints that the phase transition to MBL might largely be determined by SN and its fluctuations. Notably, the recent experiments [A. Lukin et al., Science 364, 256 (2019); J. Leonard et al., Nat. Phys. 19, 481 (2023)] demonstrated that this deviation can potentially be measured through the SN measurement. Furthermore, our investigations reveal that the thermalized states primarily occupy the low-energy section of the spectrum, as indicated by measures of localization length, gap ratio, and energy density distribution. This low-energy spectrum of the Bose model closely resembles the entire spectrum of the Fermi (or spin XXZ) model, accommodating a transition from the thermalized to the localized states. While, owing to the bosonic statistics, the high-energy spectrum of the model allows the formation of distinct clusters of bosons in the random potential background. We analyze the resulting eigenstate properties and briefly summarize the associated dynamics. To distinguish between the phase regions at the low and high energies, a probing quantity based on the structure of SvN is also devised.

cond-mat.dis-nn↗
arXiv2023

Nonuniform quadrupolar orders in the spin-3/2 generalized Heisenberg chain

The generation of nonuniform quadrupole states plays a crucial role in understanding various fascinating phenomena observed in the advancement of several research areas, e.g., multiferroic compounds, nonmagnetic superconductors, etc. In this work, we investigate the ground-state phase diagram of a generalized spin-3/2 bilinear-biquadratic-bicubic Heisenberg chain in the representation of multipolar operators. By numerical simulations with the large-scale density-matrix renormalization group (DMRG) method, we successfully identify a tetramerization phase and a stripe-Q phase. These phases are characterized by the emergence of nonuniform quadrupole orders resulting from the spontaneous breaking of translation symmetry. In particular, tetramerization phase refers to the quadrupole operators take a four-cycle, while the stripe-Q phase represents a striped pattern in quadrupole operators. Additionally, we demonstrate the presence of a Wess-Zumino-Witten (WZW) model with level k = 1 at the transition point between the dimerized (DM) phase and the Luttinger liquid (LL) phase, based on strong numerical findings.

cond-mat.str-el↗
arXiv2023

Phase transitions in the Haldane-Hubbard model

The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half-filling as a consensus on the presence of SU($2$) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number $C=1$, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the $C=1$ region, and serves as a quantitative benchmark for further theoretical and experimental investigations.

cond-mat.str-el↗
arXiv2023

Quasi-Monte Carlo for unbounded integrands with importance sampling

We consider the problem of estimating an expectation $ \mathbb{E}\left[ h(W)\right]$ by quasi-Monte Carlo (QMC) methods, where $ h $ is an unbounded smooth function on $ \mathbb{R}^d $ and $ W$ is a standard normal distributed random variable. To study rates of convergence for QMC on unbounded integrands, we use a smoothed projection operator to project the output of $W$ to a bounded region, which differs from the strategy of avoiding the singularities along the boundary of the unit cube $ [0,1]^d $ in 10.1137/S0036144504441573. The error is then bounded by the quadrature error of the transformed integrand and the projection error. If the function $h(\boldsymbol{x})$ and its mixed partial derivatives do not grow too fast as the Euclidean norm $|\boldsymbol{x}|$ goes to infinity, we obtain an error rate of $O(n^{-1+ε})$ for QMC and randomized QMC (RQMC) with a sample size $n$ and an arbitrarily small $ε>0$. However, the rate turns out to be $O(n^{-1+2M+ε})$ if the functions grow exponentially with a rate of $O(\exp\{M|\boldsymbol{x}|^2\})$ for a constant $M\in(0,1/2)$. Superisingly, we find that using importance sampling with t distribution as the proposal can improve the root mean squared error of RQMC from $O(n^{-1+2M+ε})$ to $O( n^{-3/2+ε})$ for any $M\in(0,1/2)$.

math.NA↗
arXiv2023

On the convergence conditions of Laplace importance sampling with randomized quasi-Monte Carlo

The study further explores randomized QMC (RQMC), which maintains the QMC convergence rate and facilitates computational efficiency analysis. Emphasis is laid on integrating randomly shifted lattice rules, a distinct RQMC quadrature, with IS,a classic variance reduction technique. The study underscores the intricacies of establishing a theoretical convergence rate for IS in QMC compared to MC, given the influence of problem dimensions and smoothness on QMC. The research also touches on the significance of IS density selection and its potential implications. The study culminates in examining the error bound of IS with a randomly shifted lattice rule, drawing inspiration from the reproducing kernel Hilbert space (RKHS). In the realm of finance and statistics, many problems boil down to computing expectations, predominantly integrals concerning a Gaussian measure. This study considers optimal drift importance sampling (ODIS) and Laplace importance sampling (LapIS) as common importance densities. Conclusively, the paper establishes that under certain conditions, the IS-randomly shifted lattice rule can achieve a near $O(N^{-1})$ error bound.

math.NA↗
arXiv2023

Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy

The Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden" continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

cond-mat.str-el↗
arXiv2023

Phase shift and magnetic anisotropy induced field splitting of impurity states in (Li1-xFex)OHFeSe superconductor

Revealing the energy and spatial characteristics of impurity induced states in superconductors is essential for understanding their mechanism and fabricating new quantum state by manipulating impurities. Here by using high-resolution scanning tunneling microscopy/spectroscopy, we investigated the spatial distribution and magnetic field response of the impurity states in (Li1-xFex)OHFeSe. We detected two pairs of strong in-gap states on the "dumbbell" shaped defects. They display clear damped oscillations with different phase shifts and a direct phase-energy correlation. These features have long been predicted for classical Yu-Shiba-Rusinov (YSR) state, which are demonstrated here with unprecedented resolution for the first time. Moreover, upon applying magnetic field, all the in-gap state peaks remarkably split into two rather than shift, and the splitting strength is field orientation dependent. Via detailed numerical model calculations, we found such anisotropic splitting behavior can be naturally induced by a high-spin impurity coupled to anisotropic environment, highlighting how magnetic anisotropy affects the behavior of YSR states.

cond-mat.supr-con↗
arXiv2023

Negative superinflating bipartite fluctuations near exceptional points in $\mathcal{PT}$-symmetric models

We investigate bipartite particle number fluctuations near the rank-$2$ exceptional points (EPs) of $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger models. Beyond a conformal field theory of massless fermions, fluctuations or equivalently compressibility is negative definite and exhibits superinflation in leading order at EPs, due to the defectiveness in the biorthogonal Hilbert space. Associated with the bipartite von Neumann entanglement entropy, a parameter in an anomalous correspondence referencing from a purely non-Hermitian limit helps characterize two inequivalent EP sets. Our work paves the way for understanding the singularity of fluctuations relevant to EPs, more promisingly detectable in experiments.

cond-mat.mes-hall↗
arXiv2023

Superdiffusive to Ballistic Transports in Nonintegrable Rydberg Chains

A common wisdom posits that transports of conserved quantities across clean nonintegrable quantum systems at high temperatures are diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter if the strong interaction limit is taken. Using Krylov-typicality and purification matrix-product-state methods, we establish the following observations for the strongly interacting version of the mixed-field Ising chain, a nonintegrable lattice model imitating the experimental Rydberg blockade array. Given the strict projection owing to the infinite density-density repulsion $V$, the chain's energy transport in the presence of a transverse field $g$ is superdiffusive at infinite temperature featured by an anomalous scaling exponent $\frac{3}{4}$, indicating the existence of a novel dynamical universality class. Imposing, in addition, a growing longitudinal field $h$ causes a drastic factorization of the whole Hilbert space into smaller subsectors, evidenced by the spectral parsing of the eigenstate entanglement. Being a consequence of this approximate symmetry, a superdiffusion-to-ballistic transport transition arises at $h\approx g$. Interestingly, all the above results persist for large but finite interactions and temperatures, provided that the strongly interacting condition $g,h\ll k_\textrm{B}T\ll V$ is fulfilled. Our predictions are verifiable by current experimental facilities.

cond-mat.str-el↗
arXiv2023

Magnetic field effects on the quantum spin liquid behaviors of NaYbS$_2$

Spin-orbit coupling is an important ingredient to regulate the many-body physics, especially for many spin liquid candidate materials such as rare-earth magnets and Kitaev materials. The rare-earth chalcogenides NaYbCh$_2$ (Ch = O, S, Se) is a congenital frustrating system to exhibit the intrinsic landmark of spin liquid by eliminating both the site disorders between Na$^{+}$ and Yb$^{3+}$ ions with the big ionic size difference and the Dzyaloshinskii-Moriya interaction with the perfect triangular lattice of the Yb$^{3+}$ ions. The temperature versus magnetic-field phase diagram is established by the magnetization, specific heat, and neutron-scattering measurements. Notably, the neutron diffraction spectra and the magnetization curve might provide microscopic evidence for a series of spin configuration for in-plane fields, which include the disordered spin liquid state, 120$^{o}$ antiferromagnet, and one-half magnetization state. Furthermore, the ground state is suggested to be a gapless spin liquid from inelastic neutron scattering, and the magnetic field adjusts the spin orbit coupling. Therefore, the strong spin-orbit coupling in the frustrated quantum magnet substantially enriches low-energy spin physics. This rare-earth family could offer a good platform for exploring the quantum spin liquid ground state and quantum magnetic transitions.

cond-mat.str-el↗
arXiv2022

Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations

Deep learning methods have achieved great success in solving partial differential equations (PDEs), where the loss is often defined as an integral. The accuracy and efficiency of these algorithms depend greatly on the quadrature method. We propose to apply quasi-Monte Carlo (QMC) methods to the Deep Ritz Method (DRM) for solving the Neumann problems for the Poisson equation and the static Schrödinger equation. For error estimation, we decompose the error of using the deep learning algorithm to solve PDEs into the generalization error, the approximation error and the training error. We establish the upper bounds and prove that QMC-based DRM achieves an asymptotically smaller error bound than DRM. Numerical experiments show that the proposed method converges faster in all cases and the variances of the gradient estimators of randomized QMC-based DRM are much smaller than those of DRM, which illustrates the superiority of QMC in deep learning over MC.

math.NA↗
arXiv2022

Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition

Can localization persist when interaction grows infinitely stronger than randomness? If so, is it many-body Anderson localization? How about the associated localization transition in the infinite-interaction limit? To tackle these questions, we study many-body localization (MBL) in a spin-chain model mimicking the Rydberg-blockade quantum simulator with both infinite-strength projection and moderate quasiperiodic modulation. Employing exact diagonalization, Krylov-typicality technique, and time-evolving block decimation, we identify evidence for a constrained MBL phase stabilized by a pure quasirandom transverse field. Remarkably, the constrained MBL transition may embody a discontinuous eigenstate phase transition, whose discontinuity nature significantly suppresses the finite-size drifts that plague most numerical studies of conventional MBL transition. Through quantum dynamics, we find that rotating the modulated field from parallel toward perpendicular to the projection axis induces an eigenstate transition between the diagonal and constrained MBL phases. Intriguingly, the entanglement-entropy growth in constrained MBL follows a double-log form, whereas it changes to a power law in approaching the diagonal limit. By unveiling the significance of confined nonlocal effects in integrals of motion of constrained MBL, we show that this newfound insulating state is not a many-body Anderson insulator. Our predictions can be tested in Rydberg experiments.

cond-mat.dis-nn↗
arXiv2022

Lieb-Robinson bound for constrained many-body localization

Study how quantum information propagates through spacetime manifold provides a means of identifying, distinguishing, and classifying novel phases of matter fertilized by many-body effects in strongly interacting systems in and out of equilibrium. Via a fuller characterization of key aspects regarding dynamic behaviors of information, we perform such an analysis on constrained many-body localization -- a newly proposed fully localized state under infinite-interaction limit -- in quasirandom Rydberg blockade spin chain models using thermal out-of-time-order commutators (OTOCs). The OTOC light cones predict a hitherto unknown Lieb-Robinson bound for constrained many-body localization, which is qualitatively different from that of unconstrained many-body Anderson insulators stabilized at weak-interaction limit. Our corroborated numeric and analytic study suggests that constrained many-body localization is a distinct dynamical eigenstate phase whose nonergodicity is beyond local-integral-of-motion phenomenology. Together, these findings consolidate the hierarchy of unconventional quantum dynamics encompassing constrained, unconstrained, and diagonal many-body-localized regimes.

cond-mat.dis-nn↗
arXiv2022

Low-energy Spin Dynamics of Quantum Spin Liquid Candidate $NaYbSe_{2}$

The family of rare earth chalcogenides $ARECh_{2}$ (A = alkali or monovalent ions, RE = rare earth, and Ch = O, S, Se, and Te) appears as an inspiring playground for studying quantum spin liquids (QSL). The crucial low-energy spin dynamics remain to be uncovered. By employing muon spin relaxation ($μ$SR) and zero-field (ZF) AC susceptibility down to 50 mK, we are able to identify the gapless QSL in $NaYbSe_{2}$, a representative member with an effective spin-1/2, and explore its unusual spin dynamics. The ZF $μ$SR experiments unambiguously rule out spin ordering or freezing in $NaYbSe_{2}$ down to 50 mK, two orders of magnitude smaller than the exchange coupling energies. The spin relaxation rate, $λ$, approaches a constant below 0.3 K, indicating finite spin excitations featured by a gapless QSL ground state. This is consistently supported by our AC susceptibility measurements. The careful analysis of the longitudinal field (LF) $μ$SR spectra reveals a strong spatial correlation and a temporal correlation in the spin-disordered ground state, highlighting the unique feature of spin entanglement in the QSL state. The observations allow us to establish an experimental H-T phase diagram. The study offers insight into the rich and exotic magnetism of the rare earth family.

cond-mat.str-el↗