Active Learning approach to simulations of Strongly Correlated Matter with the Ghost Gutzwiller Approximation

Abstract

Quantum embedding (QE) methods such as the Ghost Gutzwiller Approximation (gGA) offer a powerful approach to simulating strongly-correlated systems, but come with the computational bottleneck of computing the ground state of an auxiliary embedding Hamiltonian (EH) iteratively. In this work, we introduce an active learning (AL) framework integrated within the gGA to address this challenge. The methodology is applied to the single-band Hubbard model and results in a significant reduction in the number of instances where the EH must be solved. Through a principal component analysis (PCA), we find that the EH parameters form a low-dimensional structure that is largely independent of the geometric specifics of the systems, especially in the strongly-correlated regime. Our AL strategy enables us to discover this low-dimensionality structure on the fly, while leveraging it for reducing the computational cost of gGA, laying the groundwork for more efficient simulations of complex strongly-correlated materials.

14 pages, 13 figures

References in corpus (12)

• Quantum embedding theories
• Rotationally-invariant slave-boson formalism and momentum dependence of the quasiparticle weight
• Machine learning for many-body physics: The case of the Anderson impurity model
• Gutzwiller density functional theory for correlated electron systems
• Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
• Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model
• Quantum-embedding description of the Anderson lattice model with the ghost Gutzwiller Approximation
• Accuracy of ghost-rotationally-invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size
• Efficient computational screening of strongly correlated materials -- Multi-orbital phenomenology within the ghost Gutzwiller approximation
• Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials
• Derivation of the Ghost Gutzwiller Approximation from Quantum Embedding principles: the Ghost Density Matrix Embedding Theory
• Gaussian Process Regression Adaptive Density-Guided Approach: Towards Calculations of Potential Energy Surfaces for Larger Molecules

Cited by in corpus (2)

• Charge self-consistent density functional theory plus ghost rotationally-invariant slave-boson theory for correlated materials
• Linear Foundation Model for Quantum Embedding: Data-Driven Compression of the Ghost Gutzwiller Variational Space