scholarly journals Quantum dynamics in transverse-field Ising models from classical networks

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Markus Schmitt ◽  
Markus Heyl
Keyword(s):  
Monte Carlo ◽  
Quantum Dynamics ◽  
Transverse Field ◽  
Ising Models ◽  
Three Dimensions ◽  
Many Body ◽  
Monte Carlo Techniques ◽  
Many Body Theory ◽  
Monte Carlo Algorithms ◽  
Universal Structure

The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.

scholarly journals Sequential Monte Carlo Methods to Train Neural Network Models

2000 ◽  
Vol 12 (4) ◽  
pp. 955-993 ◽  
Author(s):  
J. F. G. de Freitas ◽  
M. Niranjan ◽  
A. H. Gee ◽  
A. Doucet
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Probability Distributions ◽  
Network Models ◽  
Computational Time ◽  
Optimization Strategy ◽  
Neural Network Models ◽  
Monte Carlo Techniques ◽  
Monte Carlo Algorithms ◽  
Importance Resampling

We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices.

Monte Carlo Simulation of Growth of Crystalline and Amorphous Silicon

1985 ◽  
Vol 63 ◽  
Author(s):  
Brian W. Dodson ◽  
Paul A. Taylor
Keyword(s):  
Monte Carlo ◽  
Interaction Model ◽  
Three Dimensions ◽  
Atomic Configuration ◽  
Potential Growth ◽  
Continuous Space ◽  
Monte Carlo Techniques ◽  
Stages Of Growth ◽  
Lennard Jones ◽  
Accurate Treatment

ABSTRACTThe authors have previously introduced a method, based on Monte Carlo techniques, for simulation of crystal growth processes in a continuous space. We have applied the method, initially used to simulate growth of two-dimensional Lennard-Jones systems, to treat growth of silicon in three dimensions. The interaction model for silicon is taken to be the recently introduced Stillinger-Weber (S-W) potential, which is a two- and threebody classical potential. Although the early stages of growth seem to be well modelled by the S-W potential, growth of even a single monolayer of epitaxial (111) silicon does not seem to be possible. Modifications to the S-W potential were considered, and found to be unacceptable physically. More accurate treatment of non-ideal atomic configuration energies is necessary to arrive at physically realistic growth simulations.

scholarly journals Ergodic and localized regions in quantum spin glasses on the Bethe lattice

2017 ◽  
Vol 375 (2108) ◽  
pp. 20160424 ◽  
Author(s):  
G. Mossi ◽  
A. Scardicchio
Keyword(s):  
Spin Glass ◽  
Spin Glasses ◽  
Quantum Dynamics ◽  
Bethe Lattice ◽  
Transverse Field ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Many Body ◽  
Spin Glass Phase ◽  
Ising Spin

By considering the quantum dynamics of a transverse-field Ising spin glass on the Bethe lattice, we find the existence of a many-body localized (MBL) region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split into a small MBL region and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

scholarly journals Simu-D: A Simulator-Descriptor Suite for Polymer-Based Systems under Extreme Conditions

2021 ◽  
Vol 22 (22) ◽  
pp. 12464
Author(s):  
Miguel Herranz ◽  
Daniel Martínez-Fernández ◽  
Pablo Miguel Ramos ◽  
Katerina Foteinopoulou ◽  
Nikos C. Karayiannis ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Three Dimensions ◽  
Extreme Conditions ◽  
General Applicability ◽  
Local Structures ◽  
Monte Carlo Algorithms ◽  
Wide Range ◽  
Atomistic Systems ◽  
Cylinders And Spheres ◽  
Varied Concentration

We present Simu-D, a software suite for the simulation and successive identification of local structures of atomistic systems, based on polymers, under extreme conditions, in the bulk, on surfaces, and at interfaces. The protocol is built around various types of Monte Carlo algorithms, which include localized, chain-connectivity-altering, identity-exchange, and cluster-based moves. The approach focuses on alleviating one of the main disadvantages of Monte Carlo algorithms, which is the general applicability under a wide range of conditions. Present applications include polymer-based nanocomposites with nanofillers in the form of cylinders and spheres of varied concentration and size, extremely confined and maximally packed assemblies in two and three dimensions, and terminally grafted macromolecules. The main simulator is accompanied by a descriptor that identifies the similarity of computer-generated configurations with respect to reference crystals in two or three dimensions. The Simu-D simulator-descriptor can be an especially useful tool in the modeling studies of the entropy- and energy-driven phase transition, adsorption, and self-organization of polymer-based systems under a variety of conditions.

scholarly journals A Comparison of Bootstrap and Monte Carlo Approaches to Testing for Symmetry in the Granger and Lee Error Correction Model

2013 ◽  
Vol 5 (5) ◽  
pp. 240-244
Author(s):  
Henry de-Graft Acquah
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Large Error ◽  
Small Error ◽  
Small Samples ◽  
Monte Carlo Techniques ◽  
Large Samples ◽  
Monte Carlo Algorithms ◽  
Power Of The Test ◽  
Simulation Results

In this paper, I investigate the power of the Granger and Lee model of asymmetry via bootstrap and Monte Carlo techniques. The simulation results indicate that sample size, level of asymmetry and the amount of noise in the data generating process are important determinants of the power of the test for asymmetry based on bootstrap and Monte Carlo techniques. Additionally, the simulation results suggest that both bootstrap and Monte Carlo methods are successful in rejecting the false null hypothesis of symmetric adjustment in large samples with small error size and strong levels of asymmetry. In large samples, with small error size and strong levels of asymmetry, the results suggest that asymmetry test based on Monte Carlo methods achieve greater power gains when compared with the test for asymmetry based on bootstrap. However, in small samples, with large error size and subtle levels of asymmetry, the results suggest that asymmetry test based on bootstrap is more powerful than those based on the Monte Carlo methods. I conclude that both bootstrap and Monte Carlo algorithms provide valuable tools for investigating the power of the test of asymmetry.

scholarly journals SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

2012 ◽  
Vol 11 (3) ◽  
pp. 739-755 ◽  
Author(s):  
Antun Balaž ◽  
Ivana Vidanović ◽  
Danica Stojiljković ◽  
Dušan Vudragović ◽  
Aleksandar Belić ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Higher Order ◽  
Many Body ◽  
Time Step ◽  
Many Body Theory ◽  
Spatial Dimensions ◽  
Mechanical Transition ◽  
Transition Amplitudes ◽  
Short Time ◽  
2D And 3D

AbstractWe present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to the maximal order p=18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schrödinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.

scholarly journals QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Phillip Weinberg ◽  
Marin Bukov
Keyword(s):  
Hubbard Model ◽  
Time Evolution ◽  
Quantum Dynamics ◽  
Free Particle ◽  
Transverse Field ◽  
Theoretical Research ◽  
Many Body ◽  
Imaginary Time ◽  
Many Body Systems ◽  
Python Package

We present a major update to QuSpin, SciPostPhys.2.1.003 – an open-source Python package for exact diagonalization and quantum dynamics of arbitrary boson, fermion and spin many-body systems, supporting the use of various (user-defined) symmetries in one and higher dimension and (imaginary) time evolution following a user-specified driving protocol. We explain how to use the new features of QuSpin using seven detailed examples of various complexity: (i) the transverse-field Ising chain and the Jordan-Wigner transformation, (ii) free particle systems: the Su-Schrieffer-Heeger (SSH) model, (iii) the many-body localized 1D Fermi-Hubbard model, (iv) the Bose-Hubbard model in a ladder geometry, (v) nonlinear (imaginary) time evolution and the Gross-Pitaevskii equation on a 1D lattice, (vi) integrability breaking and thermalizing dynamics in the translationally-invariant 2D transverse-field Ising model, and (vii) out-of-equilibrium Bose-Fermi mixtures. This easily accessible and user-friendly package can serve various purposes, including educational and cutting-edge experimental and theoretical research. The complete package documentation is available under http://weinbe58.github.io/QuSpin/index.html.

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