Vertex theory of many-fermion systems

Arthur Layzer

Arthur J. Layzer

Ikuo Ichinose, Daisuke Yoshioka

Behavior of doped fermions in Z2 gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z2 gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically-ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped-fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions. 1

Joachim Alexander Maruhn, P.‐G. Reinhard, E. Suraud

T. Ribic, Patrik Gunacker, Sergei Iskakov +5 more

We investigate the influence of self-energy diagrams beyond the two-particle vertex level within dual fermion theory. Specifically, we calculate the local three-particle vertex and construct from it selected dual fermion self-energy corrections to dynamical mean field theory. For the two-dimensional Hubbard model, the thus obtained self-energy corrections are small in the parameter space where dual fermion corrections based on the two-particle vertex only are small. However, in other parts of the parameter space, they are of a similar magnitude and qualitatively different from standard dual fermion theory. The high-frequency behavior of the self-energy correction is, surprisingly, even dominated by corrections stemming from the three-particle vertex.

José M. Arias, María Isabel Gallardo, Manuel Lozano