Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the two-dimensional Hubbard model

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

doi:10.1103/physrevb.89.195133

Cited by 27 publications

(22 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(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: 96%

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

2017

View full text Add to dashboard Cite

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...

show abstract

Section: Continuity Of the Self-energymentioning

confidence: 96%

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

2017

View full text Add to dashboard Cite

show abstract

“…Close to half band filling, the 2D Hubbard model on a square lattice is known to exhibit strong d-wave pair correlations [14]. While a rigorous proof that dwave superconductivity exists in the model at T = 0 is lacking, the preponderance of evidence from numerical calculations [15][16][17][18][19][20][21][22][23][24][25][26][27], as well as weak and intermediate coupling renormalization group studies [28][29][30][31][32][33][34][35], strongly support this conclusion. Rather less is known with high confidence at larger interaction U , further away from the half-filled state, or with regard to subleading pair channels throughout the phase diagram.…”

Section: Introductionmentioning

confidence: 99%

Pairing in the two-dimensional Hubbard model from weak to strong coupling

Rømer

Maier

Kreisel

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study the evolution of the leading superconducting instabilities of the single-orbital Hubbard model on a two-dimensional square lattice as a function of onsite Coulomb repulsion U and band filling by calculating the irreducible particle-particle scattering vertex obtained from dynamical cluster approximation (DCA) calculations, and compare the results to both perturbative Kohn-Luttinger (KL) theory as well as the widely used random phase approximation (RPA) spin-fluctuation pairing scheme. Near half-filling we find remarkable agreement of the hierarchy of the leading pairing states between these three methods, implying adiabatic continuity between weak-and strong-coupling pairing solutions of the Hubbard model. The d x 2 −y 2 -wave instability is robust to increasing U near half-filling as expected. Away from half filling, the predictions of KL and RPA at small U for transitions to other pair states agree with DCA at intermediate U as well as recent diagrammatic Monte Carlo calculations. RPA results fail only in the very dilute limit, where it yields a dxy ground state instead of a p-wave state established by diagrammatic Monte Carlo and low-order perturbative methods, as well as our DCA calculations. We discuss the origins of this discrepancy, highlighting the crucial role of the vertex corrections neglected in the RPA approach. Overall, comparison of the various methods over the entire phase diagram strongly suggests a smooth crossover of the superconducting interaction generated by local Hubbard interactions between weak and strong coupling.I.

show abstract

“…However, large-scale cluster DMFT calculations [59][60][61] have provided evidence that the superconductivity exhibited by the plaquette DMFT is not just an artefact of the approximation, but indeed exists also for larger clusters. The stripe and FFLO states have also been investigated within real-space DMFT calculations where correlations do not extend beyond a single site [62][63][64][65][66], but inhomogeneous solutions are allowed.…”

Section: Introductionmentioning

confidence: 99%

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

Vanhala

Törmä

2018

Phys. Rev. B

View full text Add to dashboard Cite

We use cellular dynamical mean-field theory with extended unit cells to study the ground state of the two-dimensional repulsive Hubbard model at finite doping. We calculate the energy of states where d-wave superconductivity coexists with spatially nonuniform magnetic and charge order and find that they are energetically favored in a large doping region as compared to the uniform solution. We also study the spatial form of the density and the superconducting and magnetic order parameters at different doping values.

show abstract

Two-particle correlations in a dynamic cluster approximation with continuous momentum dependence: Superconductivity in the two-dimensional Hubbard model

Cited by 27 publications

References 24 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

Pairing in the two-dimensional Hubbard model from weak to strong coupling

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

Contact Info

Product

Resources

About