Enhancing robustness and efficiency of density matrix embedding theory via semidefinite programming and local correlation potential fitting

Abstract

Density matrix embedding theory (DMET) is a powerful quantum embedding method for solving strongly correlated quantum systems. Theoretically, the performance of a quantum embedding method should be limited by the computational cost of the impurity solver. However, the practical performance of DMET is often hindered by the numerical stability and the computational time of the correlation potential fitting procedure, which is defined on a single-particle level. Of particular difficulty are cases in which the effective single-particle system is gapless or nearly gapless. To alleviate these issues, we develop a semidefinite programming (SDP) based approach that can significantly enhance the robustness of the correlation potential fitting procedure compared to the traditional least squares fitting approach. We also develop a local correlation potential fitting approach, which allows one to identify the correlation potential from each fragment independently in each self-consistent field iteration, avoiding any optimization at the global level. We prove that the self-consistent solutions of DMET using this local correlation potential fitting procedure are equivalent to those of the original DMET with global fitting. We find that our combined approach, called L-DMET, in which we solve local fitting problems via semidefinite programming, can significantly improve both the robustness and the efficiency of DMET calculations. We demonstrate the performance of L-DMET on the 2D Hubbard model and the hydrogen chain. We also demonstrate with theoretical and numerical evidence that the use of a large fragment size can be a fundamental source of numerical instability in the DMET procedure.

arXiv comment36 pages, 9 figures

References in corpus (26)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Phonons and related properties of extended systems from density-functional perturbation theory
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• CVXPY: A Python-Embedded Modeling Language for Convex Optimization
• Density matrix embedding: A strong-coupling quantum embedding theory
• Quantum embedding theories
• A practical guide to density matrix embedding theory in quantum chemistry
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• Pushing Configuration-Interaction to the Limit: Towards Massively Parallel MCSCF Calculations
• Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory
• Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Gapless quantum spin liquid, stripe and antiferromagnetic phases in frustrated Hubbard models in two dimensions
• Phase diagram of the two-dimensional extended Hubbard model: Phase transitions between different pairing symmetries when charge and spin fluctuations coexist
• Numerical Methods for the Inverse Problem of Density Functional Theory
• Can Density Matrix Embedding Theory with the Complete Activate Space Self-Consistent Field Solver Describe Single and Double Bond Breaking in Molecular Systems?
• Efficient Formulation of Ab Initio Quantum Embedding in Periodic Systems: Dynamical Mean-Field Theory
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective
• Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver
• Cluster Density Matrix Embedding Theory for Quantum Spin Systems
• Projected Density Matrix Embedding Theory with Applications to the Two-Dimensional Hubbard Model
• Block product density matrix embedding theory for strongly correlated spin systems

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• A unified density-matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation
• Comparative study of the density matrix embedding theory for the Hubbard models
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