Self-Energy Dispersion in the Hubbard Model

Abstract

We introduce the concept of self-energy dispersion as an error bound on local theories and apply it to the two-dimensional Hubbard model on the square lattice at half-filling. Since the self-energy has no single-particle analog and is not directly measurable in experiments, its general behavior as a function of momentum is an open question. In this article we benchmark the momentum dependence with the Two-Particle Self-Consistent approach together with analytical and numerical considerations and we show that through the addition of a local single-particle potential to the Hubbard model the self-energy can be flattened, such that it is essentially described by only a frequency-dependent term. We use this observation to motivate that local theories, such as the dynamical mean-field theory, should be expected to give very accurate results in the presence of a potential of this kind. Finally, we propose a simple energy argument as an estimator for the crossover from non-local to local self-energies, which can be computed even by local theories such as dynamical mean-field theory.

arXiv comment6 pages, 6 figures

References in corpus (26)

• A continuous-time solver for quantum impurity models
• The ALPS project release 1.3: open source software for strongly correlated systems
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Cluster Perturbation Theory for Hubbard models
• From band insulator to Mott insulator in one dimension
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Quantum Monte Carlo Study of an Interaction-Driven Band Insulator to Metal Transition
• Topological phase transitions in the repulsively interacting Haldane-Hubbard model
• Fluctuation driven topological Hund insulators
• Theory of spin and charge fluctuations in the Hubbard model
• Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
• Metallic phase in the two-dimensional ionic Hubbard model
• On the separability of dynamical and non-local correlations in three dimensions
• Interaction-Induced Topological and Magnetic Phases in the Hofstadter-Hubbard Model
• Superconductivity in correlated BEDT-TTF molecular conductors: critical temperatures and gap symmetries
• Probing the bond order wave phase transitions of the ionic Hubbard model by superlattice modulation spectroscopy
• Phase Diagram of the Half-Filled Ionic Hubbard Model
• Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
• Orientational bond and Néel order in the two-dimensional ionic Hubbard model
• Finite-temperature phase transitions in the ionic Hubbard model
• Superconductivity from Doublon Condensation in the Ionic Hubbard Model
• Topological insulator on honeycomb lattices and ribbons without inversion symmetry
• Existence of charge-density waves in two-dimensional ionic Hubbard model

Cited by in corpus (6)

• Effect of non-local correlations on the electronic structure of LiFeAs
• Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model
• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• On the Spatial Locality of Electronic Correlations in LiFeAs
• Anisotropy of electronic correlations: On the applicability of local theories to layered materials
• Engineering Topological Phases Guided by Statistical and Machine Learning Methods