Large-scale Monte Carlo Simulations Research Articles

Solid-liquid transition of skyrmions in a two-dimensional chiral magnet

We study the melting of skyrmions in a two-dimensional Heisenberg chiral magnet with bi-axial Dzyaloshinskii--Moriya interactions. These topological excitations may form at zero temperature a triangular crystal with long-range positional order. However, we show using large-scale Monte Carlo simulations that at small finite temperature, the skyrmions rather form a typical two-dimensional solid: Positional correlations decay with distance as power laws while the orientational correlations remain finite. At higher temperature, we observe a direct transition from this two-dimensional solid to a liquid with short-range correlations. This differs from generic two-dimensional homogeneous particle systems, where a hexatic phase is realized between the solid and the liquid.

Accelerating Molecular Dynamics Simulations with Population Annealing.

Population annealing is a powerful tool for large-scale MonteCarlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors, and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

Population annealing molecular dynamics with adaptive temperature steps

Population annealing is a novel generalized-ensemble simulation scheme used in large-scale parallel Monte Carlo simulations of disordered spin systems and similar problems. In a recent publication we proposed a generalization of this method to molecular dynamics simulations of biopolymers. In the present article we review this work and introduce a scheme for automatically choosing the temperature steps based on the observed distribution of potential energies in the population of simulated replica.

Finding new grain forms in three dimensions

Topological grain forms in three dimensions are studied experimentally and by large-scale Potts model Monte Carlo simulation. Some new band-faced grain forms are firstly observed among 16,254 pure iron grains, yet none of them is found among 28,049 Monte Carlo simulation grains, which indicate that there is shorter residence times for band-faced grain forms in three dimensions. The combined curvature/topology analysis suggests a possible efficient way of topological transitions of grain forms which is different from the known transition paths.

Superfluid density and compressibility at the superfluid-Mott glass transition

Systems of disordered interacting bosons with particle-hole symmetry can undergo a quantum phase transition between the superfluid phase and the Mott glass phase which is a gapless incompressible insulator. We employ large-scale Monte Carlo simulations of a two-dimensional site-diluted quantum rotor model to investigate the properties of the superfluid density and the compressibility at this transition. We find that both quantities feature power-law critical behavior with exponents governed by generalized Josephson relations.

Corrected-Hill versus partially reduced-bias value-at-risk estimation

The value-at-risk (VaR) at a small level q, , is the size of the loss that occurs with a probability q. Semi-parametric partially reduced-bias (PRB) VaR-estimation procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p any real number, are put forward. After the study of their asymptotic behavior, these PRB VaR-estimators are altogether compared with the classical ones for finite samples, through a large-scale Monte-Carlo simulation study. A brief application to financial log-returns is provided, as well as some final remarks.

Parallel loop cluster quantum Monte Carlo simulation of quantum magnets based on global union-find graph algorithm

A large-scale parallel loop cluster quantum Monte Carlo simulation is presented. On 24,576 nodes of the K computer, one loop cluster Monte Carlo update of the world-line configuration of the S=1∕2 antiferromagnetic Heisenberg chain with 2.6×106 spins at inverse temperature 3.1×105 is executed in about 8.62 s, in which global union-find cluster identification on a graph of about 1.1 trillion vertices and edges is performed. By combining the nonlocal global updates and the large-scale parallelization, we have virtually achieved about 1013-fold speed-up from the conventional local update Monte Carlo simulation performed on a single core. We have estimated successfully the antiferromagnetic correlation length and the magnitude of the first excitation gap of the S=4 antiferromagnetic Heisenberg chain for the first time as ξ=1.040(7)×104 and Δ=7.99(5)×10−4, respectively.

Halon: A quasiparticle featuring critical charge fractionalization

The halon is a special critical state of an impurity in a quantum-critical environment. The hallmark of the halon physics is that a well-defined integer charge gets fractionalized into two parts: a microscopic core with half-integer charge and a critically large halo carrying a complementary charge of $\pm 1/2$. The halon phenomenon emerges when the impurity--environment interaction is fine-tuned to the vicinity of a boundary quantum critical point (BQCP), at which the energies of two quasiparticle states with adjacent integer charges approach each other. The universality class of such BQCP is captured by a model of pseudo-spin-$1/2$ impurity coupled to the quantum-critical environment, in such a way that the rotational symmetry in the pseudo-spin $xy$-plane is respected, with a small local "magnetic" field along the pseudo-spin $z$-axis playing the role of control parameter driving the system away from the BQCP. On the approach to BQCP, the half-integer projection of the pseudo-spin on its $z$-axis gets delocalized into a halo of critically divergent radius, capturing the essence of the phenomenon of charge fractionalization. With large-scale Monte Carlo simulations, we confirm the existence of halons---and quantify their universal features---in O(2) and O(3) quantum critical systems.

Dynamical signature of fractionalization at a deconfined quantum critical point

Deconfined quantum critical points govern continuous quantum phase transitions at which fractionalized (deconfined) degrees of freedom emerge. Here we study dynamical signatures of the fractionalized excitations in a quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum critical point with emergent O(4) symmetry. By means of large-scale quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation functions, we obtain the dynamic spin structure factors in the $S^{x}$ and $S^{z}$ channels. In both channels, we observe broad continua that originate from the deconfined excitations. We further identify several distinct spectral features of the deconfined quantum critical point, including the lower edge of the continuum and its form factor on moving through the Brillouin Zone. We provide field-theoretical and lattice model calculations that explain the overall shapes of the computed spectra, which highlight the importance of interactions and gauge fluctuations to explaining the spectral-weight distribution. We make further comparisons with the conventional Landau O(2) transition in a different quantum magnet, at which no signatures of fractionalization are observed. The distinctive spectral signatures of the deconfined quantum critical point suggest the feasibility of its experimental detection in neutron scattering and nuclear magnetic resonance experiments.

How Small-World Interactions Can Lead to Improved Quantum Annealer Designs

There are many factors that influence the design of quantum annealing processing units. Here we address the issue of improving quantum annealing processing unit designs from the point of view of the critical behavior of spin glasses. It has been argued [Phys. Rev. X 4, 021008 (2014)] that among the most difficult Ising spin-glass ground-state problems are those related to lattices which exhibit a finite-temperature spin-glass transition. Here, we show that adding small-world couplers between qubits (spins) to the native quasi-planar quantum processing unit graph results in a topology where a disordered Ising system can undergo a finite-temperature spin-glass transition, even when an Ising spin glass on the quasi-planar native graph does not display a transition into a glassy phase at any finite temperature. To ensure that these systems can be engineered with current fabrication techniques, using large-scale Monte Carlo simulations we demonstrate that highly-constrained systems restricted to a few fabrication layers and with fixed coupler angles can also exhibit a finite-temperature spin-glass transition. This indicates that these systems might be mean-field-like, which also means that embedding highly-nonplanar problems might be simplified when compared to the underlying native topology. Our results are illustrated using the quasi-planar Chimera topology currently used in the D-Wave Systems Inc. quantum annealing machines, as well as standard two-dimensional square lattices. The presented approach can be generalized to other topologies.

Nonordinary edge criticality of two-dimensional quantum critical magnets

Based on large-scale quantum Monte Carlo simulations, we examine the correlations along the edges of two-dimensional semi-infinite quantum critical Heisenberg spin-$1/2$ systems. In particular, we consider coupled quantum spin-dimer systems at their bulk quantum critical points, including the columnar-dimer model and the plaquette-square lattice. The alignment of the edge spins strongly affects these correlations and the corresponding scaling exponents, with remarkably similar values obtained for various quantum spin-dimer systems. We furthermore observe subtle effects on the scaling behavior from perturbing the edge spins that exhibit the genuine quantum nature of these edge states. Our observations furthermore challenge recent attempts that relate the edge spin criticality to the presence of symmetry-protected topological phases in such quantum spin systems.

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene

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 Kekul\'e pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekul\'e valence bond solid phase is continuous and belongs to chiral XY universality class.

Two universality classes of the Ziff-Gulari-Barshad model with CO desorption via time-dependent Monte Carlo simulations

We study the behavior of the phase transitions of the Ziff-Gullari-Barshad (ZGB) model when the $CO$ molecules are adsorbed on the catalytic surface with a rate $y$ and desorbed from the surface with a rate $k$. We employ large-scale nonequilibrium Monte Carlo simulations along with an optimization technique based on the coefficient of determination, in order to obtain an overview of the phase transitions of the model in the whole spectrum of $y$ and $k$: ($0\leq y\leq 1$ and $0\leq k\leq 1$) with precision $\Delta y=\Delta k=0.001$. Sucessive refinements reveal a region of points belonging to the directed percolation universality class whereas the exponents $\theta $ and $\beta /\nu_{\parallel }$ obtained agree with those of this universality class. On the other hand, the effects of allowing the $CO$ desorption from the lattice on the discontinuous phase transition point of the original ZGB model suggest the emergence of an Ising-like point previously predicted in Ref. \cite{tome1993}. We show that such a point appears after a sequence of two lines of pseudo-critical points which leads to a unique peak of the coefficient of determination curve in $y_{c}=0.554$ and $k_{c}=0.064$. In this point, the exponent $\theta $ agrees with the value found for Ising model.

Effects of external forcing on evolutionary games in complex networks.

How did cooperation evolve in a complex network is an intensely investigated problem. Many mechanisms that promote cooperation have been proposed within the framework of the evolutionary game theory. Motivated by the fact that people in society or even a certain group are often controlled by a variety of simple rules, we present an external forcing mechanism to analyze the underlying reasons of widespread cooperation in this paper. In detail, we model the agents on a simple regular network, on which the learning method is controlled by external forcing mechanism, and prisoner's dilemma has been applied to describe the interaction of agents. By conducting large-scale Monte Carlo simulations, we can easily draw a conclusion that this mechanism can promote cooperation efficiently. In addition, we also show that the proposed mechanism is effective for the cooperation promotion for other game models, such as snowdrift game and multigames. Taken together, the mechanism of external forcing on the evolutionary game is a strong promoter of cooperation even under a severe temptation condition, which has a practical significance and will provide new insight into the analysis and control of cooperative strategy in the complex network for the further research.

Majorana corner modes in a second-order Kitaev spin liquid

Higher-order topological insulators are distinguished by the existence of topologically protected modes with codimension two or higher. Here, we report the manifestation of a second-order topological insulator in a two dimensional frustrated quantum magnet, which exhibits topological corner modes. Our exactly-solvable model is a generalization of the Kitaev honeycomb model to the Shastry-Sutherland lattice that, besides a chiral spin liquid phase, exhibits a gapped spin liquid with Majorana corner modes, which are protected by two mirror symmetries. This second-order Kitaev spin liquid remains stable in the presence of thermal fluctuations and undergoes a finite-temperature phase transition evidenced in large-scale quantum Monte Carlo simulations.

Quantum critical behavior of a three-dimensional superfluid-Mott glass transition

The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\nu = 1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of $p_c = 0.688392$, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents $z=1.67(6)$, $\nu = 0.90(5)$, $\beta/\nu = 1.09(3)$, and $\gamma/\nu = 2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.

Diagnosing Fractionalization from the Spin Dynamics of Z_{2} Spin Liquids on the Kagome Lattice by Quantum MonteCarlo Simulations.

Based on large-scale quantum MonteCarlo simulations, we examine the dynamical spin structure factor of the Balents-Fisher-Girvin kagome lattice spin-1/2 model, which is known to harbor an extended Z_{2} quantum spin liquid phase. We use a correlation-matrix sampling scheme combined with a stochastic analytic continuation method to resolve the spectral functions of this anisotropic quantum spin model with a three-site unit cell. Based on this approach, we monitor the spin dynamics throughout the phase diagram of this model, from the XY-ferromagnetic region to the Z_{2} quantum spin liquid regime. In the latter phase, we identify a gapped two-spinon continuum in the transverse scattering channel, which is faithfully modeled by an effective spinon tight-binding model. Within the longitudinal channel, we identify gapped vison excitations and exhibit indications for the translational symmetry fractionalization of the visons via an enhanced spectral periodicity.

Quantum Spin Liquid with Even Ising Gauge Field Structure on Kagome Lattice.

Employing large-scale quantum MonteCarlo simulations, we study the extended XXZ model on the kagome lattice. A Z_{2} quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance among three symmetry-breaking phases including stripe solid, staggered solid, and ferromagnet. This Z_{2} spin liquid is stabilized by an extended interaction related to the Rokhsar-Kivelson potential in the quantum dimer model limit. The phase transitions from the staggered solid to a spin liquid or ferromagnet are found to be first order and so is the transition between the stripe solid and ferromagnet. However, the transition between a spin liquid and ferromagnet is found to be continuous and belongs to the 3D XY^{*} universality class associated with the condensation of spinons. The transition between a spin liquid and stripe solid appears to be continuous and associated with the condensation of visons.

Quantum Monte Carlo study of the long-range site-diluted XXZ model as realized by polar molecules

Motivated by recent experiments with ultracold polar molecules trapped in deep optical lattices, we study ground-state properties of the long-ranged XXZ model with and without off-diagonal disorder. We map the spin model to a hard-core Bose-Hubbard model and perform large-scale Monte Carlo simulations by the Worm algorithm. In absence of disorder, we find that, for large enough interaction, three phases are stabilized: a superfluid phase, a checkerboard solid phase, only present at density n = 0.5, and a checkerboard supersolid phase which can be reached by doping the CB phase away from half-filling. In the presence of off-diagonal disorder and at fixed density n=0.5, we find that, unlike what observed in the case of short-range hopping, localization never occurs even for site dilution larger than the percolation threshold, and off-diagonal order, though strongly suppressed, persists for arbitrarily large values of site-dilution.

Understanding cooperative behavior of agents with heterogeneous perceptions in dynamic networks

In reality, social diversity is omnipresent. Motivated by the fact that different agents may get different perceptions for the same social dilemma, we extended the concept of heterogeneous perceptions to dynamically varying network and investigate the impact on the evolution of cooperation in this paper. Here, the heterogeneous perceptions of different agents are modeling by spatial multigames, which are characterized by two different social dilemmas: the traditional prisoners’ dilemma and the snowdrift game. The dynamic network, on the other hands, is a network whose link weights are coevolved with game strategy. By conducting large-scale Monte Carlo simulations, we draw a conclusion that for small temptation a large value of network evolution strength warrants an optimal resolution of social dilemma; while for large temptation an intermediate value of network evolution strength is the most beneficial for the evolution of cooperation. In addition, numerical simulations also indicate that the higher the value of the proportion of the snowdrift game is, the more widespread cooperative behavior becomes except for some small fluctuations. Taken together, our results support that the agents with heterogeneous perceptions in dynamic network are strong facilitators of cooperation promotion, which will provide a new insight for the further research.