Worm Algorithm Research Articles

Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

We construct energy-optimized resonating valence bond wavefunctions as a means to sketch out the zero-temperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest- (J1) and next-nearest-neighbour (J2) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J2/J1 ~ 1/2 and whose exact nature is still controversial) but on exploring whether and how the Marshall sign structure breaks down in the vicinity of the phase boundaries. Numerical evaluation of two- and four-spin correlation functions is carried out stochastically using a worm algorithm that has been modified to operate in either of two modes: one in which the sublattice labelling is fixed beforehand and another in which the worm manipulates the current labelling so as to sample various sign conventions. Our results suggest that the disordered phase evolves continuously out of the (pi,pi) Neel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (pi,0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the results of a level crossing.

Surface worm algorithm for abelian Gauge–Higgs systems on the lattice

The Prokof’ev–Svistunov worm algorithm was originally developed for models with nearest neighbor interactions that in a high temperature expansion are mapped to systems of closed loops. In this work we present the surface worm algorithm (SWA) which is a generalization of the worm algorithm concept to abelian Gauge–Higgs models on a lattice which can be mapped to systems of surfaces and loops (dual representation). Using Gauge–Higgs models with gauge groups Z3 and U(1) we compare the SWA to the conventional approach and to a local update in the dual representation. For the Z3 case we also consider finite chemical potential where the conventional representation has a sign problem which is overcome in the dual representation. For a wide range of parameters we find that the SWA clearly outperforms the local update.

Spectroscopy in finite density lattice field theory: An exploratory study in the relativistic Bose gas

We analyze 2-point functions in the relativistic Bose gas on the lattice, i.e., a charged scalar ϕ4 field with chemical potential μ. Using a generalized worm algorithm we perform a Monte Carlo simulation in a dual representation in terms of fluxes where the complex action problem is overcome. We explore various aspects of lattice spectroscopy at finite density and zero temperature, such as the asymmetry of forward and backward propagation in time and the transition into the condensed phase. It is shown that after a suitable subtraction the exponents for forward and backward propagation are independent of μ and agree with the mass obtained from the propagator at μ=0. This holds for μ<μc and shows that below the condensation transition the mass is independent of μ as expected from the Silver Blaze scenario.

Worm Algorithm for Abelian Gauge-Higgs Models

We present the surface worm algorithm (SWA) which is a generalization of the Prokof'ev Svistunov worm algorithm to perform the simulation of the dual representation (surfaces and loops) of Abelian gauge-Higgs models on a lattice. We compare the SWA to a local Metropolis update in the dual representation and show that the SWA outperforms the local update for a wide range of parameters.

A21 複数自律ロボットの連携による協調移動手法(M-OS13-4:宇宙ロボットの高度な移動システムII,M-OS13 宇宙機・宇宙ロボットのダイナミクスと制御,「海を越え,国を越え,世代を超えて!」)

Recently, many studies have been conducted on robot positioning using self-localization method without GPS. One of the efficient methods is called SLAM, Simultaneous Localization And Mapping. This method can estimate robot position with high accuracy by using both internal sensors such as gyro sensor, rotary encoder, and external sensors such as camera sensor to get landmark information. In the SLAM method, robot have to find and detect some landmarks with own camera sensor, but it needs high performance CPU and wide angle camera lens system, and it became an issue for downsizing of robot. To tackle this issue, we propose a novel method called generalized measuring worm algorithm. Fundamental idea of this algorithm is mutual positioning using two robots. We applied a pair of robots for estimating position each other, and made maps using each robot's position as landmarks. Robots equip a two dimension maker that are known size and shape beforehand for distance and direction measuring. Our method assumes a situation of two robots set on line. We call a robot of backward mother robot, while forward child robot. At a first step of measuring, mother robot try to take a photo of child robot's 2D marker, calculates distance, and get direction information by using size and shape of marker. Next step, mother robot sends a command to child robot for correcting child robot direction by using information in mother robot's sight. After child robot correcting, mother robot moves toward child robot nearly. By repeating this operation, two robots can move to any destination. They also can estimate positioning; making maps of any coordinate system based mother robot's coordinate system. To validate effectively of our method, we made an experimental system, and we could show that our method can estimate position and make maps with less than 5% error.

Quantum phases of hard-core bosons on two-dimensional lattices with anisotropic dipole-dipole interaction

By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the $y$ direction on the two-dimensional $xy$ plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an $O(N)$ Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.

Lattice study of the Silver Blaze phenomenon for a charged scalar [formula omitted] field

We analyze a complex scalar field with ϕ4 interaction and a chemical potential μ on the lattice. An exact flux representation of the partition sum is used which avoids the complex action problem and based on a generalized worm algorithm we can run Monte Carlo simulations at arbitrary densities. We study thermodynamical quantities as a function of the chemical potential μ for zero and finite temperature. It is shown that at zero temperature thermodynamical observables are independent of μ up to a critical value μc (Silver Blaze phenomenon). In a spectroscopy calculation we cross-check that μc agrees with the mass m of the scalar field. The Silver Blaze region ends in a second order phase transition and we show that for low temperatures the second order phase boundary persists and separates a pseudo Silver Blaze region from a condensed phase with strong μ-dependence.

WORM ALGORITHM PATH INTEGRAL MONTE CARLO APPLIED TO THE 3He–4He II SANDWICH SYSTEM

We present a numerical investigation of the thermal and structural properties of the 3 He –4 He sandwich system adsorbed on a graphite substrate using the worm algorithm path integral Monte Carlo (WAPIMC) method [M. Boninsegni, N. Prokof'ev and B. Svistunov, Phys. Rev. E74, 036701 (2006)]. For this purpose, we have modified a previously written WAPIMC code originally adapted for 4 He on graphite, by including the second 3 He -component. To describe the fermions, a temperature-dependent statistical potential has been used. This has proven very effective. The WAPIMC calculations have been conducted in the millikelvin temperature regime. However, because of the heavy computations involved, only 30, 40 and 50 mK have been considered for the time being. The pair correlations, Matsubara Green's function, structure factor, and density profiles have been explored at these temperatures.

Finite-temperature auxiliary-field quantum Monte Carlo technique for Bose-Fermi mixtures

We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi auxiliary-field quantum Monte Carlo (BFAFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in the BFAFQMC algorithm. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand the BFAFQMC algorithm's reach. This algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.

Monte Carlo study of the universal area distribution of clusters in the honeycomb O(n) loop model

We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0.5, 1, 1.5, and 2. At the critical point, the number of clusters, whose enclosed area is greater than A, is proportional to A−1 with a proportionality constant C. We confirm numerically that C is universal, and its value agrees well with the predictions based on the Coulomb gas method.

Computational study of a multistep height model

An equilibrium random surface multistep height model proposed in [Abraham and Newman, EPL 86, 16002 (2009)] is studied using a variant of the worm algorithm. In one limit, the model reduces to the two-dimensional Ising model in the height representation. When the Ising model constraint of single height steps is relaxed, the critical temperature and critical exponents are continuously varying functions of the parameter controlling height steps larger than one. Numerical estimates of the critical exponents can be mapped via a single parameter, the Coulomb gas coupling, to the exponents of the O(n) loop model on the honeycomb lattice with n ≤ 1.

Worm algorithms for the 3-state Potts model with magnetic field and chemical potential

We discuss worm algorithms for the 3-state Potts model with external field and chemical potential. The complex phase problem of this system can be overcome by using a flux representation where the new degrees of freedom are dimer and monomer variables. Working with this representation we discuss two different generalizations of the conventional Prokof’ev–Svistunov algorithm suitable for Monte Carlo simulations of the model at arbitrary chemical potential and evaluate their performance.

The [formula omitted] loop model on a three-dimensional lattice

We study a class of loop models, parameterized by a continuously varying loop fugacity n, on the hydrogen peroxide lattice, which is a three-dimensional cubic lattice of coordination number 3. For integer n>0, these loop models provide graphical representations for n-vector models on the same lattice, while for n=0 they reduce to the self-avoiding walk problem. We use worm algorithms to perform Monte Carlo studies of the loop model for n=0, 0.5, 1, 1.5, 2, 3, 4, 5 and 10 and obtain the critical points and a number of critical exponents, including the thermal exponent yt, magnetic exponent yh, and loop exponent yl. For integer n, the estimated values of yt and yh are found to agree with existing estimates for the three-dimensional O(n) universality class. The efficiency of the worm algorithms is reflected by the small value of the dynamic exponent z, determined from our analysis of the integrated autocorrelation times.

Critical properties of the three-dimensional XY model in large-scale Monte-Carlo simulations

The critical properties of the three-dimensional XY model are studied in large-scale Monte-Carlo simulations by using a worm algorithm for the integer-current representation of the model. In large systems, singular behavior of the internal energy around the critical point is observed, and the finite-size scaling analyses of the superfluid stiffness lead us to find the critical inverse temperature Kc = 0.45416(1) and the correlation length critical exponent ν = 0.6708(5).

Boson Pairing and Unusual Criticality in a GeneralizedXYModel

We discuss the unusual critical behavior of a generalized XY model containing both 2π-periodic and π-periodic couplings between sites, allowing for ordinary vortices and half-vortices. The phase diagram of this system includes both single-particle condensate and pair-condensate phases. Using a field theoretic formulation and worm algorithm MonteCarlo simulations, we show that in two dimensions it is possible for the system to pass directly from the disordered (high temperature) phase to the single particle (quasi)condensate via an Ising transition, a situation reminiscent of the "deconfined criticality" scenario.

Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region (J<0). In the J→-∞ limit, we map the AT model onto a fully packed loop-dimer model on the honeycomb lattice. On the basis of this exact transformation and the low-temperature expansion, we formulate a variant of worm-type algorithms for the AT model, which significantly suppress the critical slowing down. We analyze the Monte Carlo data by finite-size scaling, and locate a line of critical points of the Ising universality class in the region J<0 and K>0, with K the four-spin interaction. Further, we find that, in the J→-∞ limit, the critical line terminates at the decoupled point K=0. From the numerical results and the exact mapping, we conjecture that this "tricritical" point (J→-∞,K=0) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as z=0.28(1) near (J→-∞,K=0).

Mott-insulator-SF transition lobe in the presence of a second superfluid component

A two-component bosonic mixture loaded in a two-dimensional optical lattice is analyzed. By means of Mean-Field techniques and Worm algorithm Monte Carlo simulations, we study the effect of the presence of a second minority superfluid component on the first Mott lobe. We observe a reduction of the latter and different renormalization of the two boundaries. Our results are of interest for current experimental setups.

QCD Phase Diagram According to the Center Group

We study an effective theory for QCD at finite temperature and density which contains the leading center symmetric and center symmetry breaking terms. The effective theory is studied in a flux representation where the complex phase problem is absent and the model becomes accessible to Monte Carlo techniques also at finite chemical potential. We simulate the system by using a generalized Prokof'ev-Svistunov worm algorithm and compare the results to a low temperature expansion. The phase diagram is determined as a function of temperature, chemical potential, and quark mass. The shape and quark mass dependence of the phase boundaries are as expected for QCD. The transition into the deconfined phase is smooth throughout, without any discontinuities or critical points.

Performance of a worm algorithm in [formula omitted] theory at finite quartic coupling

Worm algorithms have been very successful with the simulation of sigma models with fixed length spins which result from scalar field theories in the limit of infinite quartic coupling λ. Here we investigate closer their algorithmic efficiency at finite and even vanishing λ for the one component model in dimensions D=2,3,4.

Quantum Monte Carlo method for pairing phenomena: Supercounterfluid of two-species Bose gases in optical lattices

We study the supercounterfluid (SCF) states in the two-component hard-core Bose-Hubbard model on a square lattice, using the quantum Monte Carlo method based on the worm (directed-loop) algorithm. Since the SCF state is a state of a pair condensation characterized by $\ensuremath{\langle}{a}^{\ifmmode\dagger\else\textdagger\fi{}}b\ensuremath{\rangle}\ensuremath{\ne}0,\ensuremath{\langle}a\ensuremath{\rangle}=0$, and $\ensuremath{\langle}b\ensuremath{\rangle}=0$, where $a$ and $b$ are the order parameters of the two components, it is important to study behaviors of the pair-correlation function $\ensuremath{\langle}{a}_{i}{b}_{i}^{\ifmmode\dagger\else\textdagger\fi{}}{a}_{j}^{\ifmmode\dagger\else\textdagger\fi{}}{b}_{j}\ensuremath{\rangle}$. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair correlation, we confirm the Kosterlitz-Thouless character of the SCF phase. The simulation efficiency is also improved in the SCF phase.