Dynamical cluster approximation with continuous lattice self-energy

Staar, Peter; Maier, Thomas; Schulthess, T. C.

doi:10.1103/physrevb.88.115101

Cited by 42 publications

(53 citation statements)

References 59 publications

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“…(B22a). While the DCA self-energy is piecewise constant in the Brillouin zone (with discontinuities at the patch edges), the cluster TRILEX selfenergy is continuous by construction, similarly to what is achieved by the DCA + method 91,92 , but without arbitrary interpolation schemes.…”

Section: Continuity Of the Self-energymentioning

confidence: 97%

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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Section: Continuity Of the Self-energymentioning

confidence: 97%

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

2017

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“…A number of extensions of DMFT have been recently proposed, formally based on the LWF, such as cluster (for reviews, see e.g. [6][7][8]) and diagrammatic [9] extensions, the DMFT+GW method [10,11], the dynamical vertex approximation (DΓA) [12], DCA + [13], etc. There are two ways to justify the formalism and propose a formal construction of the LWF Φ[G], whose closed-form expression is unattainable in general.…”

Section: The Use Of Functionals ω[G] φ[G] σ[G]mentioning

confidence: 99%

Nonexistence of the Luttinger-Ward Functional and Misleading Convergence of Skeleton Diagrammatic Series for Hubbard-Like Models

2015

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The Luttinger-Ward functional Φ [G], which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function G, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy Σ[G] ∝ δΦ[G]/δG is not a single-valued functional of G: in addition to the physical solution for Σ [G], there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for Σ in terms of G is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the non-interacting Green's function G0 converges to the correct physical branch of Σ in all cases currently accessible by diagrammatic Monte Carlo. Besides their conceptual importance, these observations have important implications for techniques based on the explicit summation of diagrammatic series.

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“…In particular, the dynamical mean-field theory (DMFT) [42], which becomes exact in infinite spatial dimensions, is a suitable tool to study dynamical properties of the lattice models. In fact, the DMFT and its extensions have been extensively applied to the attractive Hubbard model [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. Among the results, for strong coupling, a pseudogap in the spectral function has been found above T c [52][53][54][55][56].…”

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confidence: 99%

Hidden fermionic excitation in the superconductivity of the strongly attractive Hubbard model

et al. 2015

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We scrutinize the real-frequency structure of the self-energy in the superconducting state of the attractive Hubbard model within the dynamical mean-field theory. Within the strong-coupling superconducting phase which has been understood in terms of the Bose-Einstein condensation in the literature, we find two qualitatively different regions crossing over each other. In one region close to zero temperature, the self-energy depends on the frequency only weakly at low energy. On the other hand, in the region close to the critical temperature, the self-energy shows a pole structure. The latter region becomes more dominant as the interaction becomes stronger. We reveal that the self-energy pole in the latter region is generated by a coupling to a hidden fermionic excitation. The hidden fermion persists in the normal state, where it yields a pseudogap. We compare these properties with those of the repulsive Hubbard model relevant for high-temperature cuprate superconductors, showing that hidden fermions are a key common ingredient in strongly correlated superconductivity.PACS numbers: 67.85. Lm, 71.10.Fd A range of metals show superconductivity below a critical temperature (T c ), at which paired electrons acquire a spatial coherence. In conventional superconductors, the pairing mechanism is well described by the Bardeen-CooperSchrieffer (BCS) theory [1]. However, the BCS theory does not straightforwardly apply when the attractive interaction between electrons is strong. In this case, the electron pairing occurs at a temperature higher than T c and superconductivity arises when the electron pairs (regarded as composite bosons) go through the Bose-Einstein condensation (BEC) at a lower temperature [2]. Such superconductivity in the BEC regime has been explored for ultracold fermionic atom systems [3][4][5]. In fact, tightly-bound pairs [6] and an associated pseudogap behavior [7,8] have been observed for 40 K gas in the strongly-interacting region. A recent experiment also suggested that the superconductivity in FeSe is in the BCS-BEC crossover regime [9]. The preformed pairing has also been proposed in the context of cuprate high-T c superconductors [10,11]. Although it looks unlikely that the preformed pairing solely can explain the whole pseudogap behavior in the cuprates [12][13][14][15], it may be relevant in a region close to T c around the optimal doping [16,17].On the theoretical side, the crossover from BCS to BEC [5,[18][19][20] has been intensively studied with continuous [21][22][23][24][25][26][27] or lattice [28-41] fermion models, both of which give a similar phase diagram. The latter is, however, more tractable with numerical simulations and allows us to employ nonperturbative methods to study this problem. In particular, the dynamical mean-field theory (DMFT) [42], which becomes exact in infinite spatial dimensions, is a suitable tool to study dynamical properties of the lattice models. In fact, the DMFT and its extensions have been extensively applied to the attractive Hubbard model [43][44][45][4...

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Dynamical cluster approximation with continuous lattice self-energy

Cited by 42 publications

References 59 publications

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

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

Nonexistence of the Luttinger-Ward Functional and Misleading Convergence of Skeleton Diagrammatic Series for Hubbard-Like Models

Hidden fermionic excitation in the superconductivity of the strongly attractive Hubbard model

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