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

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 In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem.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.Comment: 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

Two-dimensional geometry of spin excitations in the high-transition-temperature superconductor YBa2Cu3O6+x

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Heavy d-electron quasiparticle interference and real-space electronic structure of Sr₃Ru₂O₇

The intriguing idea that strongly interacting electrons can generate spatially inhomogeneous electronic liquid-crystalline phases is over a decade old1, 2, 3, 4, 5, but these systems still represent an unexplored frontier of condensed-matter physics. One reason is that visualization of the many-body quantum states generated by the strong interactions, and of the resulting electronic phases, has not been achieved. Soft condensed-matter physics was transformed by microscopies that enabled imaging of real-space structures and patterns. A candidate technique for obtaining equivalent data in the purely electronic systems is spectroscopic imaging scanning tunnelling microscopy (SI-STM). The core challenge is to detect the tenuous but 'heavy' momentum (k)-space components of the many-body electronic state simultaneously with its real-space constituents. Sr3Ru2O7 provides a particularly exciting opportunity to address these issues. It possesses a very strongly renormalized 'heavy' d-electron Fermi liquid6, 7 and exhibits a field-induced transition to an electronic liquid-crystalline phase8, 9. Finally, as a layered compound, it can be cleaved to present an excellent surface for SI-STM

Spin dynamics in the pseudogap state of a high-temperature superconductor

The pseudogap is one of the most pervasive phenomena of high temperature superconductors. It is attributed either to incoherent Cooper pairing setting in above the superconducting transition temperature Tc, or to a hidden order parameter competing with superconductivity. Here we use inelastic neutron scattering from underdoped YBa(2)Cu(3)O(6.6) to show that the dispersion relations of spin excitations in the superconducting and pseudogap states are qualitatively different. Specifically, the extensively studied "hour glass" shape of the magnetic dispersions in the superconducting state is no longer discernible in the pseudogap state and we observe an unusual "vertical" dispersion with pronounced in-plane anisotropy. The differences between superconducting and pseudogap states are thus more profound than generally believed, suggesting a competition between these two states. Whereas the high-energy excitations are common to both states and obey the symmetry of the copper oxide square lattice, the low-energy excitations in the pseudogap state may be indicative of collective fluctuations towards a state with broken orientational symmetry predicted in theoretical work.Comment: 6 pages, 8 figures, contains supplementary information. Some data from V. Hinkov et al., arXiv:cond-mat/0601048, is include