Dual parquet scheme for the two-dimensional Hubbard model: Modeling low-energy physics of high- Tc cuprates with high momentum resolution

Abstract

We present a new method to treat the two-dimensional (2D) Hubbard model for parameter regimes which are relevant for the physics of the high-Tc superconducting cuprates. Unlike previous attempts to attack this problem, our new approach takes into account all fluctuations in different channels on equal footing and is able to treat reasonable large lattice sizes up to 32x32. This is achieved by the following three-step procedure: (i) We transform the original problem to a new representation (dual fermions) in which all purely local correlation effects from the dynamical mean field theory are already considered in the bare propagator and bare interaction of the new problem. (ii) The strong 1/(iν) 2 decay of the bare propagator allows us to integrate out all higher Matsubara frequencies besides the lowest using low order diagrams. The new effective action depends only on the two lowest Matsubara frequencies which allows us to, (iii) apply the two-particle self-consistent parquet formalism, which takes into account the competition between different low-energy bosonic modes in an unbiased way, on much finer momentum grids than usual. In this way, we were able to map out the phase diagram of the 2D Hubbard model as a function of temperature and doping. Consistently with the experimental evidence for hole-doped cuprates and previous dynamical cluster approximation calculations, we find an antiferromagnetic region at low-doping and a superconducting dome at higher doping. Our results also support the role of the van Hove singularity as an important ingredient for the high value of Tc at optimal doping. At small doping, the destruction of antiferromagnetism is accompanied by an increase of charge fluctuations supporting the scenario of a phase separated state driven by quantum critical fluctuations.

The Bethe-Salpeter equation at the critical end-point of the Mott transition

“…This is in agreement with what is known qualitatively from investigations of the Density of States: the difference between the insulator and the metal is that the latter has a quasiparticle peak at the Fermi level. Astretsov et al [62] used a single Matsubara frequency approximation to study the cuprates, our result here is a direct quantitative proof that this kind of approximation is justified at the critical end point of the Mott transition. At T < T c and U c1 < U < U c2 , the Bethe-Salpeter equation is convergent (and the iterative scheme is attractive) at both the metallic and the insulating solutions, λ < 1, and divergent (repulsive) at the unstable fixed point, λ > 1.…”

Tiling with triangles: parquet and $GWγ$ methods unified

“…The bare interaction is itself interaction-reducible and hence included in the ∆ α 's; thus we need to subtract 2U α in Eq. (10) to prevent an overcounting. As already discussed in Section II, U t = W t = ∆ t = 0.…”

“…The parquet approach [4][5][6][7][8][9][10] classifies vertex corrections into three scattering channels, allowing an unbiased competition between the bosonic fluctuations in these channels [11][12][13][14][15]. The Hedin equations, on the other hand, aim at the particle-hole channel, with vertex corrections γ in this channel being calculated selfconsistently from the derivative of the self-energy with respect to the Green's function δΣ/δG [16,17].…”

“…[39] where the parquet equations for dual fermions [40] have been reformulated. Instead, here we show how the standard parquet approach [4][5][6][7][8][9][10] can be rewritten and connected with the Hedin equations [41]. An efficient real fermion parquet solver for a quantum impurity model is presented and made available [42].…”

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

“…The specific application of the SBE formalism to the fRG presented here relies on the partial bosonization of the vertex function [35][36][37], similar to the channel decomposition [3,[38][39][40][41][42] already adopted in the context of fRG and parquet solvers [24,43] (for recent developments in this direction see also Refs. [44][45][46][47]). In addition to the screened interaction, a fermion-boson Yukawa coupling [48,49] (or Hedin vertex [50]) is determined from the vertex asymptotics, similarly to the construction of the kernel functions describing the high-frequency asymptotics, see Ref.…”