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arXiv2021

A comment on "Discrete time crystals: rigidity, criticality, and realizations"

The Letter by N. Y. Yao et. al. [1,2] presents three models for realizing a many-body localized discrete time-crystal (MBL DTC): a short-ranged model [1], its revised version [2], as well as a long-range model of a trapped ion experiment [1,3]. We show that none of these realize an MBL DTC for the parameter ranges quoted in Refs. [1,2]. The central phase diagrams in [1] therefore cannot be reproduced. The models show rapid decay of oscillations from generic initial states, in sharp contrast to the robust period doubling dynamics characteristic of an MBL DTC. Long-lived oscillations from special initial states (such as polarized states) can be understood from the familiar low-temperature physics of a static transverse field Ising model, rather than the nonequilibrium physics of an eigenstate-ordered MBL DTC. Our results on the long-range model also demonstrate, by extension, the absence of an MBL DTC in the trapped ion experiment of Ref. [3].

cond-mat.dis-nn↗

arXiv2021

Simple exponential acceleration of the power iteration algorithm

Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies on the idea that repeated multiplication of a randomly chosen vector x by the matrix A gradually amplifies the component of the vector along the eigenvector of the largest eigenvalue of A while suppressing all other components. Unfortunately, the power iteration algorithm may demonstrate slow convergence. In this report, we demonstrate an exponential speed up in convergence of the power iteration algorithm with only a polynomial increase in computation by taking advantage of the commutativity of matrix multiplication.

math.NA↗

arXiv2021

U(1) dynamics in neuronal activities

Neurons convert the external stimuli into action potentials, or spikes, and encode the contained information into the biological nerve system. Despite the complexity of neurons and the synaptic interactions in between, the rate models are often adapted to describe neural encoding with modest success. However, it is not clear whether the firing rate, the reciprocal of the time interval between spikes, is sufficient to capture the essential feature for the neuronal dynamics. Going beyond the usual relaxation dynamics in Ginzburg-Landau theory for statistical systems, we propose the neural activities can be captured by the U(1) dynamics, integrating the action potential and the ``phase" of the neuron together. The gain function of the Hodgkin-Huxley neuron and the corresponding dynamical phase transitions can be described within the U(1) neuron framework. In addition, the phase dependence of the synaptic interactions is illustrated and the mapping to the Kinouchi-Copelli neuron is established. It suggests that the U(1) neuron is the minimal model for single-neuron activities and serves as the building block of the neuronal network for information processing.

q-bio.NC↗

arXiv2021

TAP equations are repulsive

We show that for low enough temperatures, but still above the AT line, the Jacobian of the TAP equations for the SK model has a macroscopic fraction of eigenvalues outside the unit interval. This provides a simple explanation for the numerical instability of the fixed points, which thus occurs already in high temperature. The insight leads to some algorithmic considerations on the low temperature regime, also briefly discussed.

math.PR↗

arXiv2021

Crystal-like Order Stabilizing Glasses: Structural Origin of Ultra-stable Metallic Glasses

Glasses are featured with a disordered amorphous structure, being opposite to crystals that are constituted by periodic lattices. In this study we report that the exceptional thermodynamic and kinetic stability of an ultra-stable binary ZrCu metallic glass, fabricated by high-temperature physical vapor deposition, originates from ubiquitous crystal-like medium range order (MRO) constituted by Voronoi polyhedron ordering with well-defined local translational symmetry beyond nearest atomic neighbors. The crystal-like MRO significantly improves the thermodynamic and kinetic stability of the glass, which is in opposition to the conventional wisdom that crystal-like order deteriorates the stability and forming ability of metallic glasses. This study unveils the structural origin of ultra-stable metallic glasses and shines a light on the intrinsic correlation of local atomic structure ordering with glass transition of metallic glasses.

cond-mat.dis-nn↗

arXiv2021

Emergent power-law interactions in disordered crystals

We derive exact results for the fluctuations in energy produced by microscopic disorder in near-crystalline athermal systems. Our formalism captures the heterogeneity in the elastic energy of polydispersed soft disks in energy-minimized configurations. We use this to predict the distribution of interaction energy between two defects in a disordered background. We show this interaction energy displays an average power-law behaviour $\langle δE \rangle \sim Δ^{-4}$ at large distances $Δ$ between the defects. These interactions upon disorder average also display the sixfold symmetry of the underlying reference crystal. Additionally, we show that the fluctuations in the interaction energy encode the athermal correlations introduced by the disordered background. We verify our predictions with energy minimized configurations of polydispersed soft disks in two dimensions.

cond-mat.soft↗

arXiv2021

The Physics of Machine Learning: An Intuitive Introduction for the Physical Scientist

This article is intended for physical scientists who wish to gain deeper insights into machine learning algorithms which we present via the domain they know best, physics. We begin with a review of two energy-based machine learning algorithms, Hopfield networks and Boltzmann machines, and their connection to the Ising model. This serves as a foundation to understand the phenomenon of learning more generally. Equipped with this intuition we then delve into additional, more "practical," machine learning architectures including feedforward neural networks, convolutional neural networks, and autoencoders. We also provide code that explicitly demonstrates training a neural network with gradient descent.

cond-mat.dis-nn↗

arXiv2022

Slow relaxation and aging in the model of randomly connected cycles network

We propose a statistical model of a large random network with high connectivity in order to describe the behavior of {\it E.\,coli} cells after exposure to acute stress. The building blocks of this network are feedback cycles typical of the genetic and metabolic networks of a cell. Each node on the cycles is a spin degree of freedom representing a component in the cell's network that can be in one of two states - active or inactive. The cycles are interconnected by regulation or by the exchange of metabolites. Stress is realized by an external magnetic field that drives the nodes into an inactive state, and the time the magnetization passes zero value for the first time represents the first division event of the cell after the stress period. The numerical and analytical solutions for this first passage problem reproduce the aging dynamics observed in the experimental data.

cond-mat.dis-nn↗

arXiv2022

Atomic structural characteristics and dynamical properties in monatomic metallic liquids via molecular dynamics simulations

Molecular dynamics simulations were performed for five monatomic metallic liquids and the atomic structural characteristics and dynamical properties were systematically investigated and compared for understanding the underlying structural basis of liquid properties, such as glass-forming ability. All simulated monatomic liquids exhibit similar structural characteristics and temperature evolution. However, the degree varies significantly in different liquids. It is found that the atomic structures in liquid Cu, Ta, and Fe are quite similar. However, liquid Ta exhibits more ordered and more densely packed structure features, with more populated icosahedral-like atomic ordering and five-fold HA indexes, less Voronoi entropy, and more regular tetrahedral configurations. Moreover, the increase of crystal-like clusters in liquid Ta slows down with decreasing temperature, and the icosahedral-like clusters increase more quickly, exceeding crystal-like ones, in contrast to other liquids. On the contrary, the atomic structures of liquid Al and Zr are more similar, much more disordered and more loosely packed. Furthermore, liquid Ta exhibits more slow and heterogeneous dynamics, which could be facilitated by the particular atomic structures of liquid Ta. Both the atomic structure and dynamics features in liquid Ta favor its glass formation. Our findings provide comprehensive structural and dynamical information for better understanding GFA and crystallization in these typical monatomic liquids.

cond-mat.dis-nn↗

arXiv2022

Dependence of the glass transition and jamming densities on spatial dimension

We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from $d =3$ to $8$, over a wide range of temperatures and densities. Employing a scaling of density-temperature dependent relaxation times, we precisely identify the density $ϕ_0$ which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between $ϕ_0$ and the athermal jamming density $ϕ_J$, small in 3 and 4 dimensions, increases with dimension, with $ϕ_0 > ϕ_J$ for $d > 4$. We compare our results with recent theoretical calculations.

cond-mat.soft↗

arXiv2022

Odd moduli of disordered odd elastic lattices

We study the effects of bond disorder on triangular and honeycomb lattices where each spring has a probability p to be odd elastic. Using an effective medium theory and numerical simulations, we uncover the behavior of odd moduli in the presence of disorder, which we interpret as a crossover between the affine response of the passive elastic backbone, and a rigidity percolation transition in the odd elastic components. Though oddness is generally robust against disorder even at low p, we find that fine-tuned features of an odd elastic honeycomb lattice are not robust against disorder.

cond-mat.soft↗

arXiv2022

The training response law explains how deep neural networks learn

Deep neural network is the widely applied technology in this decade. In spite of the fruitful applications, the mechanism behind that is still to be elucidated. We study the learning process with a very simple supervised learning encoding problem. As a result, we found a simple law, in the training response, which describes neural tangent kernel. The response consists of a power law like decay multiplied by a simple response kernel. We can construct a simple mean-field dynamical model with the law, which explains how the network learns. In the learning, the input space is split into sub-spaces along competition between the kernels. With the iterated splits and the aging, the network gets more complexity, but finally loses its plasticity.

cond-mat.dis-nn↗

arXiv2022

Tensor-networks for High-order Polynomial Approximation: A Many-body Physics Perspective

We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a high-order nonlinear dynamics modeling problem, tensor-network models are investigated and exhibit promising modeling advantages. This novel perspective establish a connection between quantum information and functional approximation, which worth further exploration in future research.

quant-ph↗

arXiv2022

Recurrent neural networks that generalize from examples and optimize by dreaming

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological information-processing, we introduce a generalized Hopfield network where pairwise couplings between neurons are built according to Hebb's prescription for on-line learning and allow also for (suitably stylized) off-line sleeping mechanisms. Moreover, in order to retain a learning framework, here the patterns are not assumed to be available, instead, we let the network experience solely a dataset made of a sample of noisy examples for each pattern. We analyze the model by statistical-mechanics tools and we obtain a quantitative picture of its capabilities as functions of its control parameters: the resulting network is an associative memory for pattern recognition that learns from examples on-line, generalizes and optimizes its storage capacity by off-line sleeping. Remarkably, the sleeping mechanisms always significantly reduce (up to $\approx 90\%$) the dataset size required to correctly generalize, further, there are memory loads that are prohibitive to Hebbian networks without sleeping (no matter the size and quality of the provided examples), but that are easily handled by the present "rested" neural networks.

cond-mat.dis-nn↗

arXiv2022

Neural annealing and visualization of autoregressive neural networks in the Newman-Moore model

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results despite their representational power and entanglement content, thus, suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman-Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman-Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

cond-mat.dis-nn↗

arXiv2022

Neural network representation for minimally entangled typical thermal states

Minimally entangled typical thermal states (METTS) are a construction that allows one to to solve for the imaginary time evolution of quantum many body systems. By using wave functions that are weakly entangled, one can take advantage of efficient representations in the form of matrix product states. We generalize these ideas to arbitrary variational wave functions and we focus, as illustration, on the particular case of restricted Boltzmann machines. The imaginary time evolution is carried out using stochastic reconfiguration (natural gradient descent), combined with Monte Carlo sampling. Since the time evolution takes place on the tangent space, deviations between the actual path in the Hilbert space and the trajectory on the variational manifold can be important, depending on the internal structure and expressivity of the variational states. We show how these differences translate into a rescaled temperature and demonstrate the application of the method to quantum spin systems in one and two spatial dimensions.

cond-mat.str-el↗

arXiv2024

Physics-integrated Neural Network for Quantum Transport Prediction of Field-effect Transistor

Quantum-mechanics-based transport simulation is of importance for the design of ultra-short channel field-effect transistors (FETs) with its capability of understanding the physical mechanism, while facing the primary challenge of the high computational intensity. Traditional machine learning is expected to accelerate the optimization of FET design, yet its application in this field is limited by the lack of both high-fidelity datasets and the integration of physical knowledge. Here, we introduced a physics-integrated neural network framework to predict the transport curves of sub-5-nm gate-all-around (GAA) FETs using an in-house developed high-fidelity database. The transport curves in the database are collected from literature and our first-principles calculations. Beyond silicon, we included indium arsenide, indium phosphide, and selenium nanowires with different structural phases as the FET channel materials. Then, we built a physical-knowledge-integrated hyper vector neural network (PHVNN), in which five new physical features were added into the inputs for prediction transport characteristics, achieving a sufficiently low mean absolute error of 0.39. In particular, ~98% of the current prediction residuals are within one order of magnitude. Using PHVNN, we efficiently screened out the symmetric p-type GAA FETs that possess the same figures of merit with the n-type ones, which are crucial for the fabrication of homogeneous CMOS circuits. Finally, our automatic differentiation analysis provides interpretable insights into the PHVNN, which highlights the important contributions of our new input parameters and improves the reliability of PHVNN. Our approach provides an effective method for rapidly screening appropriate GAA FETs with the prospect of accelerating the design process of next-generation electronic devices.

cond-mat.dis-nn↗

arXiv2024

Impact of ChatGPT on the writing style of condensed matter physicists

We apply a state-of-the-art difference-in-differences approach to estimate the impact of ChatGPT's release on the writing style of condensed matter papers on arXiv. Our analysis reveals a statistically significant improvement in the English quality of abstracts written by non-native English speakers. Importantly, this improvement remains robust even after accounting for other potential factors, confirming that it can be attributed to the release of ChatGPT. This indicates widespread adoption of the tool. Following the release of ChatGPT, there is a significant increase in the use of unique words, while the frequency of rare words decreases. Across language families, the changes in writing style are significant for authors from the Latin and Ural-Altaic groups, but not for those from the Germanic or other Indo-European groups.

cs.CL↗