English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Studying the strong correlation effects in interacting Dirac fermion systemsis one of the most challenging problems in modern condensed matter physics. Thelong-range Coulomb interaction and the fermion-phonon interaction can lead to avariety of intriguing properties. In the strong-coupling regime, weak-couplingperturbation theory breaks down. The validity of $1/N$ expansion with $N$ beingthe fermion flavor is also in doubt since $N$ equals to $2$ or $4$ in realisticsystems. Here, we investigate the interaction between (1+2)- and(1+3)-dimensional massless Dirac fermions and a generic scalar boson, anddevelop an efficient non-perturbative approach to access the strong-couplingregime. We first derive a number of self-consistently coupled Ward-Takahashiidentities based on a careful symmetry analysis and then use these identitiesto show that the full fermion-boson vertex function is solely determined by thefull fermion propagator. Making use of this result, we rigorously prove thatthe full fermion propagator satisfies an exact and self-closed Dyson-Schwingerintegral equation, which can be solved by employing numerical methods. A majoradvantage of our non-perturbative approach is that there is no need to employany small expansion parameter. Our approach provides a unified theoreticalframework for studying strong Coulomb and fermion-phonon interactions. It mayalso be used to approximately handle the Yukawa coupling between fermions andorder-parameter fluctuations around continuous quantum critical points. Ourapproach is applied to treat the Coulomb interaction in undoped graphene. Wefind that the renormalized fermion velocity exhibits a logarithmicmomentum-dependence but is nearly energy independent, and that no excitonic gapis generated by the Coulomb interaction. These theoretical results areconsistent with experiments in graphene.

Nonperturbative Dyson-Schwinger equation approach to strongly interacting Dirac fermion systems