Mean-field approximation of the Hubbard model expressed in a many-body basis
arXiv:2301.03223 · doi:10.1063/5.0153076
Abstract
The effective independent-particle (mean-field) approximation of the Hubbard Hamiltonian is described in a many-body basis to develop a formal comparison with the exact diagonalization of the full Hubbard model, using small atomic chain as test systems. This allows for the development of an intuitive understanding of the shortcomings of the mean-field approximation and of how critical correlation effects are missed in this popular approach. The description in the many-body basis highlights a potential ambiguity related to the definition of the density of states. Specifically, satellite peaks are shown to emerge in the mean-field approximation, in departure from the common belief that they characterize correlation effects. The scheme emphasizes the importance of correlation and how different many-body corrections can improve the mean-field description. The pedagogical treatment is expected to make it possible for researchers to acquire an improved understanding of many-body effects as found in various areas related to electronic properties of molecules and solids, which is highly relevant to current efforts in quantum information and quantum computing.
References in corpus (24)
- The GW method
- Emergence of magnetism in graphene materials and nanostructures
- The GW compendium: A practical guide to theoretical photoemission spectroscopy
- Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods
- Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory
- Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation
- Symmetry restoration in mean-field approaches
- The Hubbard Dimer: A density functional case study of a many-body problem
- Beyond the GW approximation: combining correlation channels
- Dynamical Density-Matrix Renormalization Group for the Mott--Hubbard insulator in high dimensions
- The Hubbard model on the honeycomb lattice: from static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
- Spectra and total energies from self-consistent many-body perturbation theory
- Correlated Topological States in Graphene Nanoribbon Heterostructures
- The dynamically screened ladder approximation: Simultaneous treatment of strong electronic correlations and dynamical screening out of equilibrium
- Assessment of the GW approximation using Hubbard chains
- Entanglement, excitations and correlation effects in narrow zigzag graphene nanoribbons
- Image resonance in the many-body density of states at a metal surface
- Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model
- Introduction to Hubbard Model and Exact Diagonalization
- Spectroscopy of the Hubbard dimer: the spectral potential
- Exact and many-body perturbation solutions of the Hubbard model applied to linear chains
- Löwdin's symmetry dilemma within Green functions theory for the one-dimensional Hubbard model
- Entanglement and magnetism in high-spin graphene nanodisks
- Analytic continuation of the self-energy via Machine Learning techniques