Machine learning effective models for quantum systems

Abstract

The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We propose a machine learning approach that optimizes an effective model based on an estimation of its partition function. The success of the method is demonstrated by application to the single impurity Anderson model and double quantum dots, where non-perturbative results are obtained for the old problem of mapping to effective Kondo models. For quantum impurity parent Hamiltonians, we derive an alternative approach based on learning from observables. When mapping to minimal effective models, emergent scales may not be captured by observable learning, while partition function learning may not reproduce all observables.

arXiv comment4 Pages, 4 Figures and Supplementary Material

References in corpus (51)

• Quantum Machine Learning
• Towards A Rigorous Science of Interpretable Machine Learning
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantifying Entanglement
• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Machine learning phases of matter
• Quantum Cluster Theories
• Continuous Time Quantum Monte Carlo method for fermions
• Finding Density Functionals with Machine Learning
• Discovering Phase Transitions with Unsupervised Learning
• Quantum-enhanced machine learning
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Quantum Boltzmann Machine
• Machine Learning Phases of Strongly Correlated Fermions
• Self-Learning Monte Carlo Method
• Symmetries and many-body excited states with neural-network quantum states
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Equivalence of restricted Boltzmann machines and tensor network states
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Hamiltonian Learning and Certification Using Quantum Resources
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Mutual Information, Neural Networks and the Renormalization Group
• Learning a local Hamiltonian from local measurements
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Neural Network Renormalization Group
• Machine learning for many-body physics: The case of the Anderson impurity model
• Multi-impurity Anderson model for quantum dots coupled in parallel
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Machine learning quantum states in the NISQ era
• Predicting the Curie temperature of ferromagnets using machine learning
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-learning Monte Carlo with Deep Neural Networks
• Theory of the Anderson impurity model: The Schrieffer--Wolff transformation re--examined
• Generalized Wilson Chain for solving multichannel quantum impurity problems
• Hamiltonian Learning for Quantum Error Correction
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Kondo blockade due to quantum interference in single-molecule junctions
• Out-of-Equilibrium Kondo Effect: Response to Pulsed Fields
• Interleaved numerical renormalization group as an efficient multiband impurity solver
• Information geometric approach to the renormalisation group
• Construction of Hamiltonians by supervised learning of energy and entanglement spectra
• The renormalisation group via statistical inference
• Recommender Engine for Continuous Time Quantum Monte Carlo Methods
• Accelerated Continuous time quantum Monte Carlo method with Machine Learning

Cited by in corpus (11)

• Machine Learning for Quantum Matter
• Learning Quantum Hamiltonians from Single-qubit Measurements
• Predicting impurity spectral functions using machine learning
• Kondo effect in twisted bilayer graphene
• Automatic Differentiable Numerical Renormalization Group
• Data-Driven Dynamical Mean-Field Theory: an error-correction approach to solve the quantum many-body problem using machine learning
• Many-body quantum interference route to the two-channel Kondo effect: Inverse design for molecular junctions and quantum dot devices
• Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof
• Unsupervised Learning of Effective Quantum Impurity Models
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
• Fast evaluation of interaction integrals for confined systems with machine learning