# Intrinsic Dimension of Path Integrals: Data-Mining Quantum Criticality and Emergent Simplicity

@article{MendesSantos2021IntrinsicDO, title={Intrinsic Dimension of Path Integrals: Data-Mining Quantum Criticality and Emergent Simplicity}, author={Tiago Mendes-Santos and Adriano Angelone and Alex Rodriguez and Rosario Fazio and Marcello Dalmonte}, journal={PRX Quantum}, year={2021} }

T. Mendes-Santos*,1, 2 A. Angelone*,1, 3 Alex Rodriguez,1 R. Fazio,1, 4 and M. Dalmonte1, 3 The Abdus Salam International Centre for Theoretical Physics, strada Costiera 11, 34151 Trieste, Italy Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany SISSA, via Bonomea, 265, 34136 Trieste, Italy Dipartimento di Fisica, Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy

## Figures from this paper

## 7 Citations

The bilayer Hubbard model: analysis based on the fermionic sign problem

- Physics
- 2022

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, poten-tially, aspects of the physics of unconventional superconductors. Despite these important applica-tions,…

Estimating the Euclidean Quantum Propagator with Deep Generative Modelling of Feynman paths

- Computer SciencePhysical Review B
- 2022

This work proposes the concept of Feynman path generator, which efficiently generatesFeynman paths with fixed endpoints from a (low-dimensional) latent space, by targeting a desired density of paths in the Euclidean space-time.

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

- Computer ScienceJournal of chemical theory and computation
- 2022

This work adopts an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model and finds that the fluctuations of the water network occur in a high-dimensional space, which it characterize using a combination of both atomic descriptors and chemical-intuition-based coordinates.

Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

- Computer ScienceSciPost Physics
- 2022

This work trains a Generative Adversarial Network with the Entanglement Spectrum of a system bipartition, as extracted by means of Matrix Product States ansätze to identify gapless-to-gapped phase transitions in different one-dimensional models.

Hamming Distance and the onset of quantum criticality

- Physics
- 2021

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is…

Decoding conformal field theories: from supervised to unsupervised learning

- Education
- 2021

En-Jui Kuo,1, 2 Alireza Seif,1, 2, 3 Rex Lundgren,2, 4 Seth Whitsitt,2, 4 and Mohammad Hafezi1, 2, 5 Department of Physics, University of Maryland, College Park, MD 20742, USA Joint Quantum…

Efficient modeling of trivializing maps for lattice
ϕ4
theory using normalizing flows: A first look at scalability

- Computer SciencePhysical Review D
- 2021

The central idea is to use machine learning techniques to build (approximate) trivializing maps, i.e. field transformations that map the theory of interest into a ‘simpler’ theory in which the degrees of freedom decouple.

## References

SHOWING 1-10 OF 77 REFERENCES

{m

- GeologyACML
- 2020

The master programme in Applied Geology aims to provide comprehensive knowledge based on various branches of Geology, with special focus on Applied geology subjects in the areas of Geomorphology, Structural geology, Hydrogeology, Petroleum Geologists, Mining Geology), Remote Sensing and Environmental geology.

High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers

- Physics
- 2006

We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1/2 Heisenberg antiferromagnets in two dimensions: a bilayer and a…

Two-dimensional frustrated
J1−J2
model studied with neural network quantum states

- Computer Science, PhysicsPhysical Review B
- 2019

This paper uses a fully convolutional neural network model as a variational ansatz to study the frustrated spin-1/2 J1-J2 Heisenberg model on the square lattice and demonstrates that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods.

Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

- Computer Science
- 2020

This work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme, and suggests direct parallelism between conventional order parameters in real space, and the intrinsic dimension in the data space.

and a at

- ChemistryThe William Makepeace Thackeray Library
- 2018

The xishacorene natural products are structurally unique apolar diterpenoids that feature a bicyclo[3.3.1] framework. These secondary metabolites likely arise from the well-studied, structurally…

[C]

- PhysicsThe Works of Thomas De Quincey, Vol. 1: Writings, 1799–1820
- 2000

In supernova (SN) spectroscopy relatively little attention has been given to the properties of optically thick spectral lines in epochs following the photosphere’s recession. Most treatments and…

From observations to complexity of quantum states via unsupervised learning

- PhysicsPhysical Review B
- 2022

This work uses unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states by determining the minimal number of parameters needed to reproduce local observations and uses this approach as an ideal diagnostics tool for data obtained from (noisy) quantum simulators.

Topological quantum phase transitions retrieved through unsupervised machine learning

- Computer Science
- 2020

The results show that the Chebyshev distance between two data points sharpens the characteristic features of topological quantum phase transitions in momentum space, while the widely used Euclidean distance is in general suboptimal.