Variational autoencoder reconstruction of complex many-body physics

Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org
Main Authors: Luchnikov, I, Ryzhov, A, Stas, P -J C, Filippov, S N, Ouerdane, H
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 09.10.2019
Subjects:
Complex systems
Complexity
Computer simulation
Ising model
Machine learning
Mathematical models
Neural networks
Numerical methods
Phase transitions
Quantum mechanics
Reconstruction
Statistical analysis
ISSN:2331-8422
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models, show limitations in scope or applicability. On the other hand, machine learning, i.e. data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks in particular have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE) -- a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data, for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1910.03957