How to read between the lines of electronic spectra: the diagnostics of fluctuations in strongly correlated electron systems

Abstract

While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is not explicitly included. Here, we present a comprehensive overview of the different approaches which have been recently developed and applied to identify the dominant two-particle scattering processes controlling the shape of the one-particle spectral functions and, in some cases, of the physical response of the system. In particular, we will discuss the underlying general idea, the common threads and the specific peculiarities of all the proposed approaches. While all of them rely on a selective analysis of the Schwinger-Dyson (or the Bethe-Salpeter) equation, the methodological differences originate from the specific two-particle vertex functions to be computed and decomposed. Finally, we illustrate the potential strength of these methodologies by means of their applications the two-dimensional Hubbard model, and we provide an outlook over the future perspective and developments of this route for understanding the physics of correlated electrons.

arXiv comment20 pages, 17 figures

References in corpus (76)

• Quantum Cluster Theories
• Functional renormalization group approach to correlated fermion systems
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Non-perturbative many-body approach to the Hubbard model and single-particle pseudogap
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Local Electronic Correlation at the Two-Particle Level
• Fate of the false Mott-Hubbard transition in two dimensions
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Mott physics and spin fluctuations: a unified framework
• Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• From infinite to two dimensions through the functional renormalization group
• Diagrammatic Monte Carlo for Correlated Fermions
• Nature of magnetic excitations in superconducting BaFe${}_{1.9}$Ni${}_{0.1}$As${}_2$
• Controlling Feynman diagrammatic expansions: physical nature of the pseudo gap in the two-dimensional Hubbard model
• Fe-based superconductors: seven years later
• Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level
• A magnetic origin for high temperature superconductivity in iron pnictides
• The Structure of the Pairing Interaction in the 2D Hubbard Model
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Breakdown of traditional many-body theories for correlated electrons
• Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation
• Non-perturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint
• Ab initio dynamical vertex approximation
• Mott physics and spin fluctuations: a functional viewpoint
• Efficient treatment of two-particle vertices in dynamical mean-field theory
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Divergences of the irreducible vertex functions in correlated metallic systems: Insights from the Anderson Impurity Model
• Quantum dynamical screening of the local magnetic moment in Fe-based superconductors
• Parquet approximation for the 4x4 Hubbard cluster
• Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
• Parquet decomposition calculations of the electronic self-energy
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Temperature dependence of the optical spectral weight in the cuprates: Role of electron correlations
• Truncated Unity Parquet Solver
• Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling
• Attractive effect of a strong electronic repulsion -- the physics of vertex divergences
• Practical consequences of Luttinger-Ward functional multivaluedness for cluster DMFT methods
• Single-boson exchange decomposition of the vertex function
• Generic optical excitations of correlated systems: $\pi$-tons
• Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Boson-Exchange Parquet Solver for dual fermions
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• Dynamical vertex approximation for nanoscopic systems
• Worm Improved Estimators in Continuous-time Quantum Monte Carlo
• Correlated starting points for the functional renormalization group
• Nonlocal correlations and spectral properties of the Falicov-Kimball model
• Parquet-like equations for the Hedin three-leg vertex
• Fluctuation diagnostic of the nodal/antinodal dichotomy in the Hubbard model at weak coupling: a parquet dual fermion approach
• Interplay between local response and vertex divergences in many-fermion systems with on-site attraction
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Self-consistent ladder D$\Gamma$A approach
• Dynamical vertex approximation for the two-dimensional Hubbard model
• Dynamical vertex approximation for the attractive Hubbard model
• Itinerancy enhanced quantum fluctuation of magnetic moments in iron-based superconductors
• On the separability of dynamical and non-local correlations in three dimensions
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Characteristic Timescales of the Local Moment Dynamics in Hund's-metals
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: Slater vs Mott-Heisenberg
• Ab initio phonon self-energies and fluctuation diagnostics of phonon anomalies: Lattice instabilities from Dirac pseudospin physics in transition metal dichalcogenides
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Dynamical Charge Susceptibility in the Hubbard Model
• Detecting a preformed pair phase: The response to a pairing forcing field
• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• Optical sum rule anomalies in the cuprates: interplay between strong correlation and electronic bandstructures
• Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations
• Fluctuation diagnostics of the finite temperature quasi-antiferromagnetic regime of the 2D Hubbard model
• Short-range charge fluctuations in the two-dimensional Hubbard model

Cited by in corpus (21)

• The Hubbard model: A computational perspective
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Magnetic correlations in infinite-layer nickelates: an experimental and theoretical multi-method study
• Non-Fermi liquid phase and linear-in-temperature scattering rate in overdoped two dimensional Hubbard model
• Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength
• Origin and fate of the pseudogap in the doped Hubbard model
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• The dynamical vertex approximation for many-electron systems with spontaneously broken SU(2)-symmetry
• Strongly correlated superconductivity with long-range spatial fluctuations
• Fluctuations analysis of the spin susceptibility: Néel ordering revisited in dynamical mean field theory
• Fermi and Luttinger arcs: two concepts, realized on one surface
• Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory
• Role of Local Ru Hexamers in Superconductivity of Ruthenium Phosphide
• General Shiba mapping for on-site four-point correlation functions
• Unambiguous fluctuation decomposition of the self-energy: pseudogap physics beyond spin fluctuations
• Linear Response Functions Respecting Ward-Takahashi Identity and Fluctuation-Dissipation Theorem within $GW$ Approximation
• Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the functional renormalization group
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Disentangling real space fluctuations: the diagnostics of metal-insulator transitions beyond single-particle spectral functions
• Comparing the effective enhancement of local and non-local spin-orbit couplings on honeycomb lattices due to strong electronic correlations