arXiv subjects

Synge Todo

Publications and source records attributed to Synge Todo.

At least 55 records · Page 3Linked to original sources

arXiv2018

Updated Core Libraries of the ALPS Project

The open source ALPS (Algorithms and Libraries for Physics Simulations) project provides a collection of physics libraries and applications, with a focus on simulations of lattice models and strongly correlated electron systems. The libraries provide a convenient set of well-documented and reusable components for developing condensed matter physics simulation codes, and the applications strive to make commonly used and proven computational algorithms available to a non-expert community. In this paper we present an update of the core ALPS libraries. We present in particular new Monte Carlo libraries and new Green's function libraries.

physics.comp-ph↗

arXiv2018

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 $2.6 \times 10^6$ spins at inverse temperature $3.1 \times 10^5$ is executed in about 8.62 seconds, 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 $10^{13}$-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 $ξ= 1.040(7) \times 10^4$ and $Δ= 7.99(5) \times 10^{-4}$, respectively.

cond-mat.str-el↗

arXiv2018

Search for Common Minima in Joint Optimization of Multiple Cost Functions

We present a novel optimization method, named the Combined Optimization Method (COM), for the joint optimization of two or more cost functions. Unlike the conventional joint optimization schemes, which try to find minima in a weighted sum of cost functions, the COM explores search space for common minima shared by all the cost functions. Given a set of multiple cost functions that have qualitatively different distributions of local minima with each other, the proposed method finds the common minima with a high success rate without the help of any metaheuristics. As a demonstration, we apply the COM to the crystal structure prediction in materials science. By introducing the concept of data assimilation, i.e., adopting the theoretical potential energy of the crystal and the crystallinity, which characterizes the agreement with the theoretical and experimental X-ray diffraction patterns, as cost functions, we show that the correct crystal structures of Si diamond, low quartz, and low cristobalite can be predicted with significantly higher success rates than the previous methods.

physics.comp-ph↗

arXiv2018

Optical Bistability in a Low Photon-Density Regime

We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time evolution operator of the quantum master equation. We investigate the optical bistability within the low photon-density regime, where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double peak structure. We compared it with the standard optical bistability between the low photon-density regime and the high photon-density regime, where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single peak structure. We discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size, and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low photon-density regime, which are qualitatively different from the standard optical bistable phenomena.

cond-mat.stat-mech↗

arXiv2017

Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction

We investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction, $J_{ij} = |\vec{r}_i -\vec{r}_j|^{-(d+σ)}$, where $d$ (=2) is the dimension of the system and $σ$ the decay exponent, by means of the order-$N$ cluster-algorithm Monte Carlo method. In particular, we focus on the upper and lower critical decay exponents, the boundaries between the mean-field-universality, intermediate, and short-range-universality regimes. At the critical decay exponents, it is found that the critical amplitude of the standard Binder ratio of magnetization exhibits the extremely slow convergence as a function of the system size. We propose more effective physical quantities, the combined Binder ratio and the self-combined Binder ratio, both of which cancel the leading finite-size corrections of the conventional Binder ratio. Utilizing these techniques, we clearly demonstrate that in two dimensions the lower and upper critical decay exponents are $σ= 1$ and 7/4, respectively, contrary to the recent Monte Carlo and the renormalization-group studies [M. Picco, arXiv:1207.1018; T. Blanchard, et al., Europhys. Lett. 101, 56003 (2013)].

cond-mat.stat-mech↗

arXiv2017

Magnetization process of the S = 1/2 two-leg organic spin-ladder compound BIP-BNO

We have measured the magnetization of the organic compound BIP-BNO (3,5'-bis(N-tert-butylaminoxyl)-3',5-dibromobiphenyl) up to 76 T where the magnetization is saturated. The S = 1/2 antiferromagnetic Heisenberg two-leg spin-ladder model accounts for the obtained experimental data regarding the magnetization curve, which is clarified using the quantum Monte Carlo method. The exchange constants on the rung and the side rail of the ladder are estimated to be J(rung)/kB = 65.7 K and J(leg)/kB = 14.1 K, respectively, deeply in the strong coupling region: J(rung)/J(leg) > 1.

cond-mat.str-el↗

arXiv2017

Crystal Structure Prediction Supported by Incomplete Experimental Data

The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of crystal structures comprising more than several tens of atoms in the unit cell still remains difficult due to the many degrees of freedom, which increase exponentially with the number of atoms. Here we show that when some experimental data is available, even if it is totally insufficient for conventional structure analysis, it can be utilized to support and substantially accelerate structure simulation. In particular, we formulate a cost function based on a weighted sum of interatomic potential energies and a penalty function referred to as "crystallinity", which is defined using limited X-ray diffraction data. This method is applied to well-known polymorphs of $\rm{SiO_2}$ with up to 96 atoms in the simulation cell to find that it reproduces the correct structures efficiently with a very limited number of diffraction peaks. The penalty function is confirmed to destabilize the local minima of the potential energy surface, which facilitates finding the correct structure. This method opens a new avenue for determining and predicting structures that are difficult to determine by conventional methods, such as surface, interface, glass, and amorphous structures.

cond-mat.mtrl-sci↗

arXiv2017

Quantum Lattice Model Solver ${\mathcal H}Φ$

${\mathcal H}Φ$ [$aitch$-$phi$] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, ${\mathcal H}Φ$ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, ${\mathcal H}Φ$ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of ${\mathcal H}Φ$. We also show the benchmark results of ${\mathcal H}Φ$ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

cond-mat.str-el↗

arXiv2015

Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain

The local Z_N quantized Berry phase for the SU(N) antiferromagnetic Heisenberg spin model is formulated. This quantity, which is a generalization of the local Z_2 Berry phase for SU(2) symmetry, has a direct correspondence to the number of singlet pairs spanning on a particular bond, and is effective as a tool to characterize and classify the various symmetry protected topological phases of one-dimensional SU(N) spin systems. We extend the path-integral quantum Monte Carlo method for the Z_2 Berry phase in order to calculate the ZN Berry phase numerically. We demonstrate our method by calculating the Z_4 Berry phase for the bond-alternating SU(4) antiferromagnetic Heisenberg chain, which is represented by the Young diagram of four columns.

cond-mat.str-el↗

arXiv2015

Stochastic approximation of dynamical exponent at quantum critical point

We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent $z$. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional $S=1/2$ quantum $XY$ model in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of the uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, $z=1$, i.e., the three-dimensional classical $XY$ universality class. Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension $(2+2)$ governs the quantum phase transition.

cond-mat.stat-mech↗

arXiv2015

Generalized Moment Method for Gap Estimation and Quantum Monte Carlo Level Spectroscopy

We formulate a convergent sequence for the energy gap estimation in the worldline quantum Monte Carlo method. The ambiguity left in the conventional gap calculation for quantum systems is eliminated. Our estimation will be unbiased in the low-temperature limit and also the error bar is reliably estimated. The level spectroscopy from quantum Monte Carlo data is developed as an application of the unbiased gap estimation. From the spectral analysis, we precisely determine the Kosterlitz-Thouless quantum phase-transition point of the spin-Peierls model. It is stablished that the quantum phonon with a finite frequency is essential to the critical theory governed by the antiadiabatic limit, i.e., the $k=1$ SU(2) Wess-Zumino-Witten model.

cond-mat.stat-mech↗

arXiv2015

Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices

We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical $XY$ model with a $Z_4$ symmetry-breaking field and the 3-state Potts model, respectively. In the square-lattice case, the thermal exponent, $ν$, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, $η$ and $γ/ν$, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the $Z_4$ symmetry-breaking field is always marginal. In contrast, $ν$ in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the $Z_3$ field remains relevant in the SU(3) and SU(4) cases.

cond-mat.stat-mech↗

arXiv2014

Parallelized Quantum Monte Carlo Algorithm with Nonlocal Worm Updates

Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size-dependence of the Bose-condensation order parameter of the hardcore Bose-Hubbard model with $L\times L\times βt = 10240\times 10240\times 16$, using 3200 computing cores, which shows good parallelization efficiency.

cond-mat.stat-mech↗

arXiv2013

Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) Néel and valence-bond solid phases is characterized for $N=2,3,$ and $4$ on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y \equiv 1/ν$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field $Ψ^2$ for the SU(3) model.

cond-mat.str-el↗

arXiv2013

Geometric Allocation Approaches in Markov Chain Monte Carlo

The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions.

cond-mat.stat-mech↗

arXiv2013

Path-integral Monte Carlo for the Gauge-fixed Berry Connection and the Local Z_2 Berry Phase

We present a general formula of the gauge-fixed Berry connection which can be evaluated by path- integral Monte Carlo method. We also propose that the gauge-fixed local Berry connection can be an- other effective tool to estimate precisely the quantum critical point. For a demonstration, we calculate the gauge-fixed Berry connection and the local Z2 Berry phase of the antiferromagnetic Heisenberg model on a staggered bond-alternating ladder, and estimated quantum critical point is consistent with other methods.

cond-mat.str-el↗

arXiv2013

Monte Carlo simulation with aspect ratio optimization: Anomalous anisotropic scaling in dimerized antiferromagnet

We present a method that optimizes the aspect ratio of a spatially anisotropic quantum lattice model during the quantum Monte Carlo simulation, and realizes the virtually isotropic lattice automatically. The anisotropy is removed by using the Robbins-Monro algorithm based on the correlation length in each direction. The method allows for comparing directly the value of critical amplitude among different anisotropic models, and identifying the universality more precisely. We apply our method to the staggered dimer antiferromagnetic Heisenberg model and demonstrate that the apparent non-universal behavior is attributed mainly to the strong size correction of the effective aspect ratio due to the existence of the cubic interaction.

cond-mat.stat-mech↗

arXiv2013

Long-Range Order of the Three-Sublattice Structure in the S = 1 Heisenberg Antiferromagnet on a Spatially Anisotropic Triangular Lattice

We study the S=1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 \simle J_2/J_1 \le 1, where J_1 is the interaction amplitude along the chains and J_2 is the amplitude of other interactions.

cond-mat.str-el↗