Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics

Gunnarsson, O.; Schäfer, Thomas; LeBlanc, James; Gull, Emanuel; Merino, Jaime; Sangiovanni, Giorgio; Rohringer, G.; Toschi, A.

doi:10.1103/physrevlett.114.236402

Cited by 139 publications

(191 citation statements)

References 104 publications

(189 reference statements)

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“…This is consistent with a common belief that Q = (π, π) spin fluctuations are very important for the physics, as well as with the fluctuation diagnostics results. 42 For the 3d Hubbard model similar physics was first proposed by Berk-Schrieffer. 43 Later spin fluctuations have been proposed to be important for the 2d Hubbard model and similar models by many groups.…”

Section: -41mentioning

confidence: 76%

“…We first discuss the vertex function, following the notations of Rohringer et al 23 and Gunnarsson et al 42 We introduce the generalized susceptibility for finite temperature T = 1/β, using the Matsubara formalism…”

Section: Formalism Model and Methodsmentioning

confidence: 99%

“…We note here that, from the merely conceptual point of view, the parquet decomposition is the most "natural" route to disentangle the physical information encoded in self-energies and correlated spectral functions. The parquet procedure can be compared, e.g., to the recently introduced fluctuation diagnostics 42 approach, which also aims at extracting the underlying physics of a given self-energy: In the fluctuation diagnostics the quantitative information about the role played by the different physical processes is extracted by studying the different representations (e.g., charge, spin, or particle-particle), in which the EOM for the self-energy, and specifically the full two-particle scattering amplitude, can be written. Hence, in this respect, the parquet decomposition provides a more direct procedure, because it does not require any further change of representation for the momentum, frequency, spin variables, and can be readily analyzed at once, provided that the vertex functions have been calculated in an channelunbiased way.…”

Section: -41mentioning

confidence: 99%

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Parquet decomposition calculations of the electronic self-energy

et al. 2016

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The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet decomposition is used to unravel the underlying physics of non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies, and hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach [Phys. Rev. Lett. 114, 236402 (2015)]. However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin-channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition, and -more generally -of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of an RVB state, which are typical hallmarks of a pseudogap state in DCA.

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Section: -41mentioning

confidence: 76%

Section: Formalism Model and Methodsmentioning

confidence: 99%

Section: -41mentioning

confidence: 99%

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Parquet decomposition calculations of the electronic self-energy

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“…Thus, converged cluster DMFT results can only be obtained at high temperatures 55 . There, detailed studies [56][57][58] point to the importance of (possibly long-ranged) spin fluctuations, calling for a unification of both classes of approaches. First steps in this direction have been accomplished by diagrammatic extensions of DMFT , and by the single-site TRILEX formalism 81,82 , which interpolates between long-range and Mott physics, and describes aspects of pseudogap physics and the d-wave superconducting dome 83 .…”

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Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters

2017

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We present an embedded-cluster method, based on the TRILEX formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, selfenergies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW +extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.Two major approaches have been put forth to fathom the nature of high-temperature superconductivity. Spin fluctuation theory [1][2][3][4][5][6][7][8] , inspired by the early experiments on cuprate compounds, is based on the introduction of phenomenological bosonic fluctuations coupled to the electrons. It belongs to a larger class of methods, including the fluctuation-exchange (FLEX) 9 and GW approximations 10,11 , or the Eliashberg theory of superconductivity 12 . In the Hubbard model, these methods can formally be obtained by decoupling the electronic interactions with Hubbard-Stratonovich (HS) bosons carrying charge, spin or pairing fluctuations. They are particularly well suited for describing the system's long-range modes. However, they suffer from two main drawbacks: without an analog of Migdal's theorem for spin fluctuations, they are quantitatively uncontrolled; worse, the results depend on the precise form of the bosonic fluctuations used to decouple the interaction term, an issue referred to as the "Fierz ambiguity" [13][14][15][16][17][18] .A second class of methods, following Anderson 19 , puts primary emphasis on the fact that the undoped compounds are Mott insulators, where local physics plays a central role. Approaches like dynamical mean field theory (DMFT) 20 and its cluster extensions 21-25 , which self-consistently map the lattice problem onto an effective problem describing a cluster of interacting atoms embedded in a noninteracting host, are tools of choice to examine Anderson's idea. Cluster DMFT has indeed been shown to give a consistent qualitative picture of cuprate physics, including pseudogap and superconducting phases . Compared to fluctuation theories, it a priori comes with a control parameter, the size N c of the embedded cluster. However, this is of limited practical use, since the convergence with N c is nonmonotonic for small N c 33 , requiring large N c 's, which cann...

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“…At the nodal point, the energy dependence of δΣ F V (k, iω) resembles that of a Fermi liquid, while at the antinodal point, δΣ F V (k, iω) gives strong scattering. It is noteworthy that this momentum dependence of δΣ F V (k, iω) also emerges from recent calculations using dynamical cluster approximation 43 , suggesting the leading order in the vertex functions captures the essential physics of the quasiparticle-paramagnon interaction. On the other hand, the SF model, which does not take into account the frequency dependence of the vertex function, overestimates the scattering in δΣ (k, iω) at both antinodal and nodal point.…”

Section: -9mentioning

confidence: 90%

Quantum critical point revisited by dynamical mean-field theory

Kotliar

Tsvelik

2017

Phys. Rev. B

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Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. By comparing with the calculations based on Spin-Fermion model, our results indicate the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor to capture the momentum dependence in quasiparticle scattering.Introduction. The interplay between quasiparticles and bosonic collective modes, in particular in the proximity of a quantum critical point (QCP) 1,2 , is believed to be a driving force behind the rich phase diagram of many correlated electronic systems 3-5 . This paper explores the connection between the quasiparticles and collective modes in a doped antiferromagnet within the framework of local dynamical mean field theory (DMFT)6 . It is known that local DMFT is not fully capable of addressing the effects of non-local correlation, which are particularly important for the critical phenomena in low-dimensional system. In this paper, however, we aim to investigate to what extent local DMFT can depict the spin fluctuations in a strongly correlated system and the possibility to construct the non-local effects from local DMFT. In fact, the formalism for two-particle response functions, although proposed in the early stage of DMFT 6 , has not been well explored to study the dynamical properties of two-particle fluctuations. Recently, an approach based on this formalism and random phase approximation (RPA) has gained success in describing the magnetic excitations in iron pnictides [7][8][9] . In this work, we make a step beyond the RPA approach by taking full account of the frequency dependence of the vertex functions, and compute the momentum dependence of excitation energy and damping rate of spin fluctuations, in hope of providing insight and guidance in interpreting the spectra of correlated materials from neutron and resonant inelastic X-ray scattering measurements (RIXS) [10][11][12][13][14][15][16] . With the two-dimensional Hubbard model as a working example, we use the vertex functions to calculate the non-local correction to the single electron self energy in the leading order of quasiparticle-paramagnon interaction. We show that the leading order correction reproduces the momentum-dependent feature that emerges from self-consistent calculation in cluster extensions of DMFT [17][18][19] . We also compare it with the non-local correction obtained by the phenomenological approach based on the Spin-Fermion (SF) model 20,21 where the vertice...

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Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics

Cited by 139 publications

References 104 publications

Parquet decomposition calculations of the electronic self-energy

Parquet decomposition calculations of the electronic self-energy

Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters

Quantum critical point revisited by dynamical mean-field theory

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