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.

Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems

“…( 43) at zero bosonic frequency and spatial momentum and evaluated at ν = ν = ν0 ≡ πT (s. also Fig. 17), as a function of the fRG scale Λ. rate or not) AF fluctuations, consistent with previous findings in fRG [3,39,85,90] and DMF 2 RG [1, 3], as well as in recent numerical analyses [63,65,105].…”

“…The aim of this section is to thoroughly inspect all terms contributing to the sizable enhancement of the susceptibility χ d , which we briefly discussed above. In the spirit of the post-processing procedures [28,[63][64][65] recently applied [15,[64][65][66]103] to several quantum manybody approaches to the Hubbard model, we decompose Eqs. (33) and (36), in order to distinguish the different contributions to the d-wave susceptibility.…”

“…III and IV we discuss the results for the susceptibilities and Yukawa couplings at half filling and out of it, providing also a comparison with the fermionic formalism. In order to identify the mechanisms responsible for strong d-wave pairing correlations, we perform a diagnostics [28,[63][64][65][66] of the corresponding fluctuations. We finally conclude with a summary and an outlook in Sec.…”

Magnetic Properties and Pseudogap Formation in Infinite-Layer Nickelates: Insights From the Single-Band Hubbard Model

“…For the DΓA we employ its ladder-version in the particle-hole (magnetic) channel with Moriyaesque λ-corrections in the spin channel [42][43][44]. This choice of the scattering channel greatly simplifies the algorithm (as it bypasses the general, but complicated, parquet treatment) and is justified in the pseudogap regime of the Hubbard model, where fluctuation diagnostics methods could demonstrate unequivocally the dominance of the spin channel on the single-particle spectrum [45][46][47][48].…”

Magnetic properties and pseudogap formation in infinite-layer nickelates: insights from the single-band Hubbard model

“…For the DΓA we employ its ladder-version in the particle-hole (magnetic) channel with Moriyaesque λ-corrections in the spin channel [37][38][39]. This choice of the scattering channel greatly simplifies the algorithm (as it bypasses the general, but complicated, parquet treatment) and is justified in the pseudogap regime of the Hubbard model, where fluctuation diagnostics methods could demonstrate unequivocally the dominance of the spin channel on the singleparticle spectrum [40][41][42][43].…”