Learning phase transitions from dynamics

Nieuwenburg, Evert van; Bairey, Eyal; Refael, Gil

doi:10.1103/physrevb.98.060301

Cited by 70 publications

(56 citation statements)

References 61 publications

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“…Neural networks have become a standard tool to tackle problems where we want to make predictions without following a particular algorithm or imposing structure on the available data (see for example [32][33][34]) and they have been applied to a wide variety of problems in physics. For example, in condensed matter physics and generally in many-body settings, neural networks have proven particularly useful to characterize phase transitions [4][5][6][7][8][9]. The aim of these works is to optimise the accuracy of the predictions, but not to extract information on what the network learned during training.…”

Section: Comparison With Previous Workmentioning

confidence: 99%

“…While neural networks have been applied to a variety of problems in physics, most work to date has focused on the efficiency or quality of predictions of neural networks, without an understanding how they solve the problem [4][5][6][7][8][9] (see Section 4.1 and [10] for a review and further references). Other algorithms and neural network architectures have been developed to produce a physical model by imposing some structure on the space of solutions and on the input data [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Discovering Physical Concepts with Neural Networks

et al. 2020

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2 These authors contributed equally to this work.While neural networks have been remarkably successful for a variety of practical problems, they are often applied as a black box, which limits their utility for scientific discoveries. Here, we present a neural network architecture that can be used to discover physical concepts from experimental data without being provided with additional prior knowledge. For a variety of simple systems in classical and quantum mechanics, our network learns to compress experimental data to a simple representation and uses the representation to answer questions about the physical system. Physical concepts can be extracted from the learned representation, namely: (1) The representation stores the physically relevant parameters, like the frequency of a pendulum.(2) The network finds and exploits conservation laws: it stores the total angular momentum to predict the motion of two colliding particles. (3) Given measurement data of a simple quantum mechanical system, the network correctly recognizes the number of degrees of freedom describing the underlying quantum state. (4) Given a time series of the positions of the Sun and Mars as observed from Earth, the network discovers the heliocentric model of the solar systemthat is, it encodes the data into the angles of the two planets as seen from the Sun. Our work provides a first step towards answering the question whether the traditional ways by which physicists model nature naturally arise from the experimental data without any mathematical and physical pre-knowledge, or if there are alternative elegant formalisms, which may solve some of the fundamental conceptual problems in modern physics, such as the measurement problem in quantum mechanics.Problem: Predict the position of a one-dimensional damped pendulum at different times. Physical model: Equation of motionSolution:Observation: Time series of positions: o = x(t i ) i∈{1,...,50} ∈ R 50 , with equally spaced t i . Mass m = 1kg, amplitude A 0 = 1m and phase δ 0 = 0 are fixed; spring constant κ ∈ [5, 10] kg/s 2 and damping factor b ∈ [0.5, 1] kg/s are varied between training samples. Question: Prediction times: q = t pred ∈ R.Correct answer: Position at time t pred : a cor = x(t pred ) ∈ R .Implementation: Network depicted in Figure 1b with 3 latent neurons. Key findings:• SciNet predicts the positions x(t pred ) with a root mean square error below 2% (with respect to the amplitude A 0 = 1m) (Figure 2a).• SciNet stores κ and b in two of the latent neurons, and does not store any information in the third latent neuron (Figure 2b).

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Section: Comparison With Previous Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discovering Physical Concepts with Neural Networks

et al. 2020

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“…To further corroborate our analysis, we apply methods from machine learning [57], which has emerged recently as a powerful tool to analyze localization phenomena [58][59][60][61][62][63], to our data obtained using the TDVP. We use two algorithms: a partially supervised approach that has previously been employed in Ref.…”

Section: Machine Learningmentioning

confidence: 99%

Many-body localization and delocalization in large quantum chains

et al. 2018

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We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to L = 100 spins, i.e., much larger than L 20 that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent β which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent βΛ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder Wc that separates the ergodic and many-body localized regimes, compared to the values of Wc in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents β and βΛ increase, with increasing L, for relatively small L but saturate for L 50, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine Wc. arXiv:1807.05051v4 [cond-mat.dis-nn]

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“…It provides an example of a generic quantum many-body system that cannot reach thermal equilibrium [4][5][6][7]. In recent years, an enormous theoretical effort was invested in understanding the nature of the MBL transition [8][9][10], the dynamical [11][12][13] and entanglement [14][15][16][17] properties of these systems and their response to external probes [18,19] and periodic driving [20][21][22]. Also the experimental community [23][24][25][26][27] has found interest in this field, in particular, because these systems have the potential of storing information about initial states for long times, and hence may implement quantum memory devices.…”

Section: Introductionmentioning

confidence: 99%

From Bloch oscillations to many-body localization in clean interacting systems

Nieuwenburg

Baum

Refael

2019

Proc. Natl. Acad. Sci. U.S.A.

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207

183

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In this work we demonstrate that non-random mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the non-interacting limit, these models show the well known Wannier-Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient, these models exhibit non-ergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a new class of generic non-random models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by employing machine learning techniques, the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.

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Learning phase transitions from dynamics

Cited by 70 publications

References 61 publications

Discovering Physical Concepts with Neural Networks

Discovering Physical Concepts with Neural Networks

Many-body localization and delocalization in large quantum chains

From Bloch oscillations to many-body localization in clean interacting systems

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