Comparison of Monte Carlo and diagrammatic calculations for the two-dimensional Hubbard model

Bulut, N.; Scalapino, D. J.; White, Steven R.

doi:10.1103/physrevb.47.2742

Cited by 104 publications

(87 citation statements)

References 14 publications

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“…3(d)) compared with the RPA (with full χ zz ) result. Our finding at U = 4 is in good agreement with the work of Bulut et al [14], which shows that the effective particle-particle interaction created by the Hubbard U increases with lowering temperature and can reach large values. Figure 4 gives for both the intermediate (U = 4) and strong correlation (U = 8) cases the doping dependence of the susceptibility χ zz (q), of the renormalization factor |γ(p, q)| 2 , and of the effective pairing interaction V (p, q).…”

supporting

confidence: 82%

Role of vertex corrections in the spin-fluctuation–mediated pairing mechanism

2005

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Abstract. -We study numerically and partly diagrammatically the renormalization of the electron-spin interaction or vertex in a two-dimensional one-band Hubbard model with spinfluctuation momentum transfer q = (π, π). We find that the renormalized electron-spin vertex decreases quite generally with decreasing temperature at all doping densities. As a combination of two concurring effects, i.e. the decrease of the vertex and the increase of the spin susceptibility, the effective pairing interaction increases with lowering temperature in the intermediatecorrelation regime, but flattens off in the strong-correlation regime. Our findings indicate that in the high-Tc cuprates the pairing mediated by antiferromagnetic spin fluctuations is substantially reduced due to vertex corrections.

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supporting

confidence: 82%

Role of vertex corrections in the spin-fluctuation–mediated pairing mechanism

2005

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“…These low-energy spin excitations near (π, π) also may be integral to pairing in a broad class of superconductors 2 , and their doping evolution will thus be well captured by both computational methods. We note that this value forŪ falls within the range of values obtained in previous studies 5,9,10 ; however, one should note again that for the chosen set of parameters the undoped, single-band Hubbard model possesses a Mott insulating ground state, and should not be viewed as weakly correlated. The expression for χ RPA c does not contain a new pole, so its behavior is primarily determined by that of χ 0 and thus set by the noninteracting bandstructure.…”

Section: Model and Methodsmentioning

confidence: 56%

Doping evolution of spin and charge excitations in the Hubbard model

et al. 2015

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To shed light on how electronic correlations vary across the phase diagram of the cuprate superconductors, we examine the doping evolution of spin and charge excitations in the single-band Hubbard model using determinant quantum Monte Carlo (DQMC). In the single-particle response, we observe that the effects of correlations weaken rapidly with doping, such that one may expect the random phase approximation (RPA) to provide an adequate description of the two-particle response. In contrast, when compared to RPA, we find that significant residual correlations in the two-particle excitations persist up to 40% hole and 15% electron doping (the range of dopings achieved in the cuprates). These fundamental differences between the doping evolution of single-and multi-particle renormalizations show that conclusions drawn from single-particle processes cannot necessarily be applied to multi-particle excitations. Eventually, the system smoothly transitions via a momentumdependent crossover into a weakly correlated metallic state where the spin and charge excitation spectra exhibit similar behavior and where RPA provides an adequate description.

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“…While some tests of the GW [24,25], TMA [25,26], or FLEX [27] approaches have been published, we still lack a clear picture about the importance of the different diagram classes, and the beneficial or detrimental effect of self-consistent partial resummations.…”

Section: Introductionmentioning

confidence: 99%

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

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We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second-order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW + DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second-order diagram. FLEX + DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

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Comparison of Monte Carlo and diagrammatic calculations for the two-dimensional Hubbard model

Cited by 104 publications

References 14 publications

Role of vertex corrections in the spin-fluctuation–mediated pairing mechanism

Role of vertex corrections in the spin-fluctuation–mediated pairing mechanism

Doping evolution of spin and charge excitations in the Hubbard model

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

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