Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ 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-$T_c$ 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 $1/(i\nu {)}^2$ 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 $T_c$ 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.

19 pages, 18 figures, stylistic changes, appendix added

References in corpus (15)

• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• New Trends in Density Matrix Renormalization
• Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa${}_2$Cu${}_3$O${}_y$
• Fate of the false Mott-Hubbard transition in two dimensions
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Observation of Dirac-like energy band and ring-torus Fermi surface associated with the nodal line in topological insulator CaAgAs
• A finite-frequency functional RG approach to the single impurity Anderson model
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• First direct observation of the Van Hove singularity in the tunneling spectra of cuprates
• Lifshitz Transition in the Two Dimensional Hubbard Model
• Role of three-particle vertex within dual fermion calculations
• High-temperature optical spectral weight and Fermi liquid renormalization in Bi-based cuprates
• The {\it victory} project v1.0: an efficient parquet equations solver

Cited by in corpus (1)

• Covariant Bethe-Salpeter approximation in strongly correlated electron systems model