Systematically improvable multiscale solver for correlated electron systems

2014/10/31 by Alexei A. Kananenka, Emanuel Gull, Dominika Zgid · 7 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Applied mathematics #Benchmark (surveying) #Computer science #Electron #Embedding #Hubbard model #Mathematics #Monte Carlo method #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum mechanics #Solver #Statistical physics #Strongly correlated material #Superconductivity #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.91.121111

published as Phys. Rev. B 91, 121111(R), 2015 · 4 pages, 5 figures

openalex publication_date 2015/03/23 · arxiv created 2015/04/22 · arxiv updated 2015/04/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe a framework for a general multiscale method based on embedding a self-energy of a strongly correlated subsystem into a self-energy generated by a method able to treat large weakly correlated systems approximately. As an example, we present the embedding of an exact diagonalization self-energy into a self-energy generated from self-consistent second-order perturbation theory. Using a quantum impurity model, generated from a cluster dynamical mean field approximation to the two-dimensional Hubbard model, as a benchmark, we illustrate that our method allows us to obtain accurate results at a fraction of the cost of typical Monte Carlo calculations. We test the method in multiple regimes of interaction strengths and dopings of the model. The general embedding framework we present avoids difficulties such as double counting corrections, frequency-dependent interactions, or vertex functions. As it is solely formulated at the level of the single-particle Green's function, it provides a promising route for the simulation of realistic materials that are currently difficult to study with other methods.

Citations

• A Collective Description of Electron Interactions. I. Magnetic Interactions
• Frequency-dependent local interactions and low-energy effective models from electronic structure calculations
• Solving the dynamical mean-field theory at very low temperatures using the Lanczos exact diagonalization
• New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
• Note on an Approximation Treatment for Many-Electron Systems
• Electronic structure calculations using dynamical mean field theory
• Continuous-time Monte Carlo methods for quantum impurity models

Cited by

• Green’s function coupled cluster formulations utilizing extended inner excitations
• Sparse modeling of large-scale quantum impurity models with low symmetries
• Emerging quantum computing algorithms for quantum chemistry
• Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Ab initio self-energy embedding for the photoemission spectra of NiO and MnO
• Finite temperature quantum embedding theories for correlated systems
• Momentum-space cluster dual-fermion method