Extracting electronic many-body correlations from local measurements with artificial neural networks

Abstract

The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We demonstrate that by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work demonstrates that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.

arXiv comment13 pages, 3 figures

References in corpus (45)

• Quantum entanglement
• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Machine learning and the physical sciences
• Entanglement detection
• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Measuring entanglement entropy through the interference of quantum many-body twins
• Calculation of reduced density matrices from correlation functions
• The ITensor Software Library for Tensor Network Calculations
• Local entanglement and quantum phase transition in the Hubbard model
• Entanglement and quantum phase transition in the extended Hubbard model
• Universality of Entropy Scaling in 1D Gap-less Models
• Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array
• Identifying topological order through unsupervised machine learning
• Imaging electrostatically confined Dirac fermions in graphene quantum dots
• Efficient real frequency solver for dynamical mean field theory
• Essential entanglement for atomic and molecular physics
• Electric-field controlled spin reversal in a quantum dot with ferromagnetic contacts
• Machine Learning for Quantum Matter
• Solving the Bose-Hubbard model with machine learning
• Bipartite entanglement entropy in fractional quantum Hall states
• Nagaoka ferromagnetism observed in a quantum dot plaquette
• Experimental Characterization of Two-Particle Entanglement through Position and Momentum Correlations
• Machine Learning for Condensed Matter Physics
• Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
• Block-block entanglement and quantum phase transitions in one-dimensional extended Hubbard model
• Real space mapping of topological invariants using artificial neural networks
• Transport through quantum-dot spin valves containing magnetic impurities
• Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model
• The Half-Filled One-Dimensional Extended Hubbard Model: Phase diagram and Thermodynamics
• Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model
• Machine learning topological phases in real space
• Single-site entanglement at superconductor-insulator transition in the Hirsch model
• Quantum Renormalization Groups Based on Natural Orbitals
• Spin-induced charge correlations in transport through interacting quantum dots with ferromagnetic leads
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model
• Quantum information analysis of the phase diagram of the half-filled extended Hubbard model
• Identifying Topological Phase Transitions in Experiments Using Manifold Learning
• Quantum well states and amplified spin-dependent Friedel oscillations in thin films
• Relating correlation measures: the importance of the energy gap
• Few-body nature of Kondo correlated ground states
• Measuring post-quench entanglement entropy through density correlations
• Machine Learning Phase Diagram in the Half-filled One-dimensional Extended Hubbard Model
• Identifying Chern numbers of superconductors from local measurements

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• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Hamiltonian-learning quantum magnets with non-local impurity tomography
• Transfer learning of many-body electronic correlation entropy from local measurements