Identifying structural changes with unsupervised machine learning methods

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering methods are applied to instantaneous radial distributions of atomic configurations from classical molecular dynamics simulations of metallic systems over a large temperature range. Principal component analysis is used to dramatically reduce the dimensionality of the feature space across the samples using an orthogonal linear transformation that preserves the statistical variance of the data under the condition that the new feature space is linearly independent. From there, k-means clustering is used to partition the samples into solid and liquid phases through a criterion motivated by the geometry of the reduced feature space of the samples, allowing for an estimation of the melting point transition. This pattern criterion is conceptually similar to how humans interpret the data but with far greater throughput, as the shapes of the radial distributions are different for each phase and easily distinguishable by humans. The transition temperature estimates derived from this machine learning approach produce comparable results to other methods on similarly small system sizes. These results show that machine learning approaches can be applied to structural changes in physical systems

The Boson-Hubbard Model on a Kagome Lattice with Sextic Ring-Exchange Terms

High order ring-exchange interactions are crucial for the study of quantum fluctuations on highly frustrated systems. We present the first exact quantum Monte Carlo study of a model of hard-core bosons with sixth order ring-exchange interactions on a two-dimensional kagome lattice. By using the Stochastic Green Function algorithm, we show that the system becomes unstable in the limit of large ring-exchange interactions. It undergoes a phase separation at all fillings, except at 1/3 and 2/3 fillings for which the superfluid density vanishes and an unusual mixed valence bond and charge density ordered solid is formed.Comment: 4 pages, 7 figure

Complex phases in the doped two-species bosonic Hubbard Model

We study a two-dimensional bosonic Hubbard model with two hard-core species away from half filling using Quantum Monte Carlo simulations. The model includes a repulsive interspecies interaction and different nearest-neighbor hopping terms for the two species. By varying the filling we find a total of five distinct phases, including a normal liquid phase at higher temperature, and four different phases at lower temperature. We find an anti-ferromagnetically ordered Mott insulator and a region of coexistent anti-ferromagnetic and superfluid phases near half filling. Further away from half filling the phase diagram displays a superfluid phase and a novel phase inside the superfluid region at even lower temperatures. In this novel phase separated region, the heavy species has a Mott behavior with integer filling, while the lighter species shows phase separated Mott and superfluid behaviors.Comment: 5 pages, 4 figure

Phase diagram of the Bose-Hubbard model on a ring-shaped lattice with tunable weak links

Motivated by recent experiments on toroidal Bose-Einstein condensates in all-optical traps with tunable weak links, we study the one-dimensional Bose-Hubbard model on a ring-shaped lattice with a small region of weak hopping integrals using quantum Monte Carlo simulations. Besides the usual Mott insulating and superfluid phases, we find a phase which is compressible but non superfluid with a local Mott region. This `local Mott' phase extends in a large region of the phase diagram. These results suggest that the insulating and conducting phases can be tuned by a local parameter which may provide a new insight to the design of atomtronic devices.Comment: 5 pages, 5 figure

Periodic Anderson model with Holstein phonons for the description of the Cerium volume collapse

Recent experiments have suggested that the electron-phonon coupling may play an important role in the $\gamma \rightarrow \alpha$ volume collapse transition in Cerium. A minimal model for the description of such transition is the periodic Anderson model. In order to better understand the effect of the electron-phonon interaction on the volume collapse transition, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling enhances the volume collapse, which is consistent with experiments in Cerium. While we start with the Kondo Volume Collapse scenario in mind, our results capture some interesting features of the Mott scenario, such as a gap in the conduction electron spectra which grows with the effective electron-phonon coupling.Comment: 8 pages, 6 figure

Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder

The 2-dimensional Ising model on a square lattice is investigated with a variational autoencoder in the non-vanishing field case for the purpose of extracting the crossover region between the ferromagnetic and paramagnetic phases. The encoded latent variable space is found to provide suitable metrics for tracking the order and disorder in the Ising configurations that extends to the extraction of a crossover region in a way that is consistent with expectations. The extracted results achieve an exceptional prediction for the critical point as well as agreement with previously published results on the configurational magnetizations of the model. The performance of this method provides encouragement for the use of machine learning to extract meaningful structural information from complex physical systems where little a priori data is available

Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional $28.4\%$ speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 picoseconds per spin flip attempt for simulating the three-dimensional Edwards-Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.Comment: 15 pages, 18 figure

Locally self-consistent embedding approach for disordered electronic systems

We present a new embedding scheme for the locally self-consistent method to study disordered electron systems. We test this method in a tight-binding basis and apply it to the single band Anderson model. The local interaction zone is used to efficiently compute the local Green's function of a supercell embeded into a local typical medium. We find a quick convergence as the size of the local interaction zone which reduces the computational costs as expected. This method captures the Anderson localization transition and accurately predicts the critical disorder strength. The present work opens the path towards the development of a typical medium embedding scheme for the $O(N)$ multiple scattering methods.Comment: 7 pages, 5 figure