Two-Particle-Self-Consistent Approach for the Hubbard Model

Abstract

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.

Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron)

References in corpus (26)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Pseudogap and charge density waves in two dimensions
• Spin correlations in the electron-doped high-transition-temperature superconductor Nd{2-x}Ce{x}CuO{4+/-delta}
• Strongly Correlated Superconductivity: a plaquette Dynamical mean field theory study
• Correlation between linear resistivity and $T_c$ in the Bechgaard salts and the pnictide superconductor Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$
• Strength of Correlations in electron and hole doped cuprates
• Laser ARPES, the sudden approximation, and quasiparticle-like peaks in Bi2Sr2CaCu2O8+delta
• Criticality in correlated quantum matter
• Finite doping signatures of the Mott transition in the two-dimensional Hubbard model
• Does Simple Two-Dimensional Hubbard Model Account for High-Tc Superconductivity in Copper Oxides?
• The Hubbard model within the equations of motion approach
• Physics of cuprates with the two-band Hubbard model - The validity of the one-band Hubbard model
• Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects
• Measurement of x-ray absorption spectra of overdoped high-temperature cuprate superconductors: Inapplicability of the single-band Hubbard model
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• Interaction-Induced Adiabatic Cooling for Antiferromagnetism in Optical Lattices
• Pseudogap in underdoped cuprates and spin-density-wave fluctuations
• Non-Perturbative Treatment of Charge and Spin Fluctuations in the Two-Dimensional Extended Hubbard Model: Extended Two-Particle Self-Consistent Approach
• The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram
• The superconducting gap in the Hubbard model and the two gap energy scales in high-Tc cuprates
• Conditions for magnetically induced singlet d-wave superconductivity on the square lattice
• Competition between charge and spin order in the $t-U-V$ extended Hubbard model on the triangular lattice
• Spectral weight of doping-induced states in the 2D Hubbard model
• Scaling and commensurate-incommensurate crossover for the d=2, z=2 quantum critical point of itinerant antiferromagnets

Cited by in corpus (7)

• Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Fermi surface transformation at the pseudogap critical point of a cuprate superconductor
• divERGe implements various Exact Renormalization Group examples
• Multi-orbital two-particle self-consistent approach -- strengths and limitations
• Quasi-particle functional Renormalisation Group calculations in the two-dimensional t-t'-Hubbard model
• Diagrammatic bosonization, aspects of criticality, and the Hohenberg-Mermin-Wagner theorem in parquet approaches