Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

Mendes-Santos, Tiago; Turkeshi, Xhek; Dalmonte, Marcello; Rodríguez, Álex

doi:10.1103/physrevx.11.011040

Cited by 47 publications

(51 citation statements)

References 60 publications

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“…phase transitions based on detecting changes in structure of a set of wave function snapshots [157,158]. In fact, the entanglement phase transition in stabilizer circuits can be seen as a data structure transition [159].…”

Section: Symmetry Breaking Transitionmentioning

confidence: 99%

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Sierant

Chiriacò

Surace

et al. 2022

Quantum

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Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

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Section: Symmetry Breaking Transitionmentioning

confidence: 99%

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Sierant

Chiriacò

Surace

et al. 2022

Quantum

View full text Add to dashboard Cite

show abstract

“…Much of the work in this area makes use of neural network models which, while unparalleled in machine learning tasks, are generally hard to interpret. But recently, among other geometric and topological approaches [16][17][18][19], there has been an interest in using persistent homology, a tool from the new field of topological data analysis (TDA), to produce interpretable features which are inherently sensitive to topological objects. These can then be compared in their own right, or fed into a machine learning model [20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

2022

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We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.

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“…45 This quantity, known as the intrinsic dimension (ID), has been successfully used to characterize changes in the conformation of proteins 46,47 as well as phase transitions in simple classical and quantum Hamiltonians. 48,49 The ID also feeds into the third and final step of our procedure in which the minima and transition states of the high-dimensional free energy landscape are located by using a density peaks clustering algorithm. [50][51][52] This procedure illustrates that, at room temperature, the free energy landscape associated with the local environment of water consists of one broad minimum that expands in several dimensions.…”

Section: Introductionmentioning

confidence: 99%

High Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning

Offei-Danso¹,

Hassanali²,

Rodriguez³

2021

Preprint

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The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model. A battery of state-of-the-art unsupervised data-science techniques are used to characterize the free energy landscape of water starting from encoding the water environment using local-atomic descriptors, through dimensionality reduction and finally the use of advanced clustering techniques. Analysis of the free energy at ambient conditions was found to be consistent with a rough single basin and independent of the choice of the water model. We find that the fluctuations of the water network occur in a high-dimensional space which we characterize using a combination of both atomic descriptors and chemical-intuition based coordinates. We demonstrate that a combination of both types of variables are needed in order to adequately capture

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Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

Cited by 47 publications

References 60 publications

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

High Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning

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