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High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks

Physical Review B 2023年第5期108卷 054410-054410页

作者： Christopher Roth Attila Szabó Allan H. MacDonald Physics Department University of Texas at Austin Austin 78712-1710 Texas Rudolf Peierls Centre for Theoretical Physics University of Oxford Oxford OX1 3PU United Kingdom ISIS Facility Rutherford Appleton Laboratory Harwell Campus Didcot OX11 0QX United Kingdom

We show that neural quantum states based on very deep (4–16-layered) neural networks can outperform state-of-the-art variational approaches on highly frustrated quantum magnets, including quantum-spin-liquid candidates. We focus on group convolutional neural networks that allow us to efficiently impose space-group symmetries on our ansätze. We achieve state-of-the-art ground-state energies for the J1−J2 Heisenberg models on the square and triangular lattices, in both ordered and spin-liquid phases, and discuss ways to access low-lying excited states in nontrivial symmetry sectors. We also compute spin and dimer correlation functions for the quantum paramagnetic phase on the triangular lattice, which do not indicate either conventional or valence-bond ordering.

关键词： Magnetic phase transitions Spin dynamics Topological materials Artificial neural networks Discrete symmetries in condensed matter metropolis algorithm Quantum Monte Carlo

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Nonparametric Power-Law Surrogates

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Physical Review X 2022年第2期12卷 021056-021056页

作者： Jack Murdoch Moore Gang Yan Eduardo G. Altmann MOE Key Laboratory of Advanced Micro-Structured Materials and School of Physics Science and Engineering Tongji University Shanghai 200092 People’s Republic of China Frontiers Science Center for Intelligent Autonomous Systems Tongji University Shanghai 200092 People’s Republic of China Center for Excellence in Brain Science and Intelligence Technology Chinese Academy of Sciences Shanghai 200031 People’s Republic of China School of Mathematics and Statistics University of Sydney Sydney New South Wales 2006 Australia

Power-law distributions are widely used in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first infer the scale exponent α using the observed data of interest and then sample from the associated distribution. This approach has important limitations because it relies on a fixed α (e.g., it has limited applicability in testing the family of power-law distributions) and on the hypothesis of independent observations (e.g., it ignores temporal correlations and other constraints typically present in complex systems data). Here we propose a constrained surrogate method that overcomes these limitations by choosing uniformly at random from a set of sequences exactly as likely to be observed under a discrete power law as the original sequence (i.e., regardless of α) and by showing how additional constraints can be imposed in the sequence (e.g., the Markov transition probability between states). This nonparametric approach involves redistributing observed prime factors to randomize values in accordance with a power-law model but without restricting ourselves to independent observations or to a particular α. We test our results in simulated and real data, ranging from the intensity of earthquakes to the number of fatalities in disasters.

关键词： Patterns in complex systems Scaling laws of complex systems metropolis algorithm Time series analysis

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Monte Carlo simulations of the thermodynamic behavior of exchange graded ferromagnets

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Physical Review B 2021年第9期103卷 094440-094440页

作者： J. S. Salcedo-Gallo L. Fallarino J. D. Alzate-Cardona E. Restrepo-Parra A. Berger Departamento de Física y Química Universidad Nacional de Colombia Manizales Colombia CIC nanoGUNE BRTA E-20018 Donostia - San Sebastián Spain

In this work, we investigate the thermodynamic behavior of exchange graded ferromagnetic films using Monte Carlo simulations. The systems are modeled by using a classical Heisenberg Hamiltonian, considering only nearest neighbor exchange interactions and a linear depth-dependent effective magnetic exchange coupling strength profile. Our quantitative assessment of the local physical quantities shows that each layer exhibits rather isolated thermodynamic behavior, since both layerwise magnetization and susceptibility data indicate layer-specific “local” Curie temperatures as a consequence of the depth-dependent change in the exchange coupling strength. We also propose and evaluate a predictive formulation for such profiles of “local” Curie temperatures, whose only input is the pre-selected exchange coupling profile. Having this very precise predictive tool, we show how it can be used to obtain the temperature-dependent ferromagnetic state including its depth-dependent magnetization profile at any given temperature. Thus, it is possible to predict which exchange profile will produce a desired thermodynamic behavior and associated functionality, without the need to perform complex experiments or time-consuming computations. With this study, we furthermore demonstrate that nonlocal aspects of the thermodynamic state formation in graded magnetic materials are relevant only over very short length scales, which is in outstanding qualitative agreement with prior numerical and experimental work.

关键词： Exchange interaction Magnetism Magnetic multilayers Methods in magnetism metropolis algorithm Monte Carlo methods

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Square skyrmion crystal in centrosymmetric itinerant magnets

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Physical Review B 2021年第2期103卷 024439-024439页

作者： Satoru Hayami Yukitoshi Motome Department of Applied Physics the University of Tokyo Tokyo 113-8656 Japan

We theoretically investigate the origin of the square-type skyrmion crystal in centrosymmetric itinerant magnets, motivated by the recent experimental findings in GdRu2Si2 [N. D. Khanh et al., Nat. Nanotech. 15, 444 (2020)]. By simulated annealing for an effective spin model derived from the Kondo lattice model on a square lattice, we find that a square skyrmion crystal composed of a superposition of two spin helices is stabilized in a magnetic field by synergy between the positive biquadratic, bond-dependent anisotropic, and easy-axis anisotropic interactions. This is in stark contrast to triangular skyrmion crystals, which are stabilized by only one of the three, suggesting that the square skyrmion crystal is characteristic of itinerant magnets with magnetic anisotropy. We also show that a variety of noncollinear and noncoplanar spin textures appear, depending on the model parameters as well as the applied magnetic field. The present systematic study will be useful not only for identifying the key ingredients in GdRu2Si2 but also for exploring further skyrmion-hosting materials in centrosymmetric itinerant magnets.

关键词： Magnetism RKKY interaction Skyrmions Spin density waves Magnetic systems Lattice models in condensed matter metropolis algorithm

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Statistical mechanics of a coevolving spin system

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Physical Review E 2018年第3期98卷 030301(R)-030301(R)页

作者： Tomasz Raducha Mateusz Wilinski Tomasz Gubiec H. Eugene Stanley Institute of Experimental Physics Faculty of Physics University of Warsaw Pasteura 5 02-093 Warsaw Poland Instituto de Fisica Interdisciplinary Sistemas Complejos IFISC (CSIC-UIB) 07122 Palma de Mallorca Spain Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa Italy Center for Polymer Studies and Department of Physics Boston University Boston Massachusetts 02215 USA

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a Hamiltonian that merges the classical Ising model and the statistical theory of correlated random networks. As a result, we obtain rich phase diagrams with different phase transitions both in the state of nodes and in the graph topology. We argue that the coupling between the spin dynamics and the structure of the network is crucial in understanding the complex behavior of real-world systems and omitting one of the approaches renders the description incomplete.

关键词： Magnetic phase transitions Network phase transitions Network structure Phase transitions Structural properties Topological phase transition Spin glasses Ising model metropolis algorithm Monte Carlo methods Network Models

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Superdiffusive quantum work and adiabatic quantum evolution in finite temperature chaotic Fermi systems

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Physical Review B 2022年第6期106卷 064201-064201页

作者： András Grabarits Márton Kormos Izabella Lovas Gergely Zaránd Department of Theoretical Physics Institute of Physics Budapest University of Technology and Economics Műegyetem rkp. 3. H-1111 Budapest Hungary MTA-BME Quantum Dynamics and Correlations Research Group Budapest University of Technology and Economics Műegyetem rkp. 3. H-1111 Budapest Hungary Kavli Institute for Theoretical Physics University of California Santa Barbara California 93106 USA

We study the full distribution of quantum work in generic, noninteracting, disordered fermionic nanosystems at finite temperature. We derive an analytical determinant formula for the characteristic function of work statistics for quantum quenches starting from a thermal initial state. For work small compared to the thermal energy of the Fermi gas, work distribution is Gaussian, and the variance of work is proportional to the average work, while in the low-temperature or large-work limit, a non-Gaussian distribution with superdiffusive work fluctuations is observed. Similarly, the time dependence of the probability of adiabaticity crosses over from an exponential to a stretched exponential behavior. For large enough average work, the work distribution becomes universal, and depends only on the temperature and the mean work. Apart from initial low-temperature transients, work statistics are well captured by a Markovian energy-space diffusion process of hardcore particles, starting from a thermal initial state. Our findings can be verified by measurements on nanoscale circuits or via single qubit interferometry.

关键词： Fluctuation theorems Heat transfer Landau-Zener effect Quantum quench Quantum statistical mechanics Quantum thermodynamics Disordered systems Quantum dots Quantum many-body systems First-principles calculations metropolis algorithm Random matrix theory Second quantization

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Two Phase Transitions in the Two-Dimensional Nematic Three-Vector Model with No Quasi-Long-Range Order: Monte Carlo Simulation of the Density of States

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Physical Review Letters 2018年第21期121卷 217801-217801页

作者： B. Kamala Latha V. S. S. Sastry School of Physics University of Hyderabad Hyderabad 500046 India Centre for Modelling Simulation and Design University of Hyderabad Hyderabad 500046 India

The presence of stable topological defects in a two-dimensional (d=2) liquid crystal model allowing molecular reorientations in three dimensions (n=3) was largely believed to induce a defect-mediated Berzenskii-Kosterlitz-Thouless-type transition to a low temperature phase with quasi-long-range order. However, earlier Monte Carlo (MC) simulations could not establish certain essential signatures of the transition, suggesting further investigations. We study this model by computing its equilibrium properties through MC simulations, based on the determination of the density of states of the system. Our results show that, on cooling, the high temperature disordered phase deviates from its initial progression towards the topological transition, crossing over to a new fixed point, condensing into a nematic phase with exponential correlations of its director fluctuations. The thermally induced topological kinetic processes continue, however, limited to the length scales set by the nematic director fluctuations, and lead to a second topological transition at a lower temperature. It is argued that in the (d=2, n=3) system with an attractive biquadratic Hamiltonian, the presence of additional molecular degrees of freedom and local Z2 symmetry associated with lattice sites together promote the onset of an additional relevant scaling field at matching length scales in the high temperature region, leading to a crossover.

关键词： Critical phenomena Exotic phases of matter Phase transitions Nematic liquid crystals Entropic sampling methods metropolis algorithm

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Monte Carlo spin simulations of magnetic noise: The search for pivoting

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Physical Review B 2024年第14期109卷 144510-144510页

作者： D. L. Mickelsen Ruqian Wu Clare C. Yu Department of Physics and Astronomy University of California Irvine California 92697 USA

Superconducting quantum interference devices (SQUIDs) show great promise as quantum bits (qubits) but continue to be hindered by flux noise. The flux noise power spectra of SQUIDs go as 1/fα, where α is the temperature-dependent noise exponent. Experiments find 0.5≲α≲1. Furthermore, experiments find that the noise power spectra versus frequency at different temperatures pivot about or cross at a common point for each SQUID. To try to better understand the results and motivated by experimental evidence that magnetic moments on the surface of SQUIDS produce flux noise, we present the results of our Monte Carlo simulations of various spin systems on 2D lattices. We find that only spin glasses produce α∼1 at low temperature. We find that aliasing of the noise power spectra at high frequencies can lead to spectral pivoting if it is in proximity to a knee at a slightly lower frequency. We show that the pivot frequency depends on the method of site selection and how often the magnetization is recorded. The spectral pivoting that occurs in our simulations is due to aliasing and does not explain the spectral pivoting of experiments.

关键词： Superconductors XY model Antiferromagnets Ferromagnets SQUID Spin glasses Superconducting qubits metropolis algorithm Monte Carlo methods

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Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland)

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WATER RESOURCES RESEARCH 2007年第10期43卷 W10401-1-W10401-1页

作者： Yang, Jing Reichert, Peter Abbaspour, Karim C. Swiss Fed Inst Aquat Sci & Technol Dubendorf Switzerland

Calibration and uncertainty analysis in hydrologic modeling are affected by measurement errors in input and response and errors in model structure. Recently, extending similar approaches in discrete time, a continuous time autoregressive error model was proposed for statistical inference and uncertainty analysis in hydrologic modeling. The major advantages over discrete time formulation are the use of a continuous time error model for describing continuous processes, the possibility of accounting for seasonal variations of parameters in the error model, the easier treatment of missing data or omitted outliers, and the opportunity for continuous time predictions. The model was developed for the Chaohe Basin in China and had some features specific for this semiarid climatic region (in particular, the seasonal variation of parameters in the error model in response to seasonal variation in precipitation). This paper tests and extends this approach with an application to the Thur River basin in Switzerland, which is subject to completely different climatic conditions. This application corroborates the general applicability of the approach but also demonstrates the necessity of accounting for the heavy tails in the distributions of residuals and innovations. This is done by replacing the normal distribution of the innovations by a Student t distribution, the degrees of freedom of which are adapted to best represent the shape of the empirical distribution of the innovations. We conclude that with this extension, the continuous time autoregressive error model is applicable and flexible for hydrologic modeling under different climatic conditions. The major remaining conceptual disadvantage is that this class of approaches does not lead to a separate identification of model input and model structural errors. The major practical disadvantage is the high computational demand characteristic for all Markov chain Monte Carlo techniques.

关键词： PARAMETER UNCERTAINTY CATCHMENT MODELS metropolis algorithm GLOBAL OPTIMIZATION COMPUTER-MODELS WATER-QUALITY INFERENCE RUNOFF TRANSFORMATIONS CALIBRATION

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Statistical mechanical model for crack growth

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Physical Review E 2024年第1期109卷 015001-015001页

作者： Michael R. Buche Scott J. Grutzik Computational Solid Mechanics and Structural Dynamics Sandia National Laboratories Albuquerque New Mexico 87185 USA Materials and Failure Modeling Sandia National Laboratories Albuquerque New Mexico 87185 USA

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

关键词： Classical statistical mechanics Growth processes Thermodynamics Continuum particle models Lattice models in statistical physics Approximation methods for many-body systems Many-body techniques metropolis algorithm Monte Carlo methods Numerical approximation & analysis

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