Numerical simulation of Dirac semimetals

Abstract

Dirac semimetals are recently discovered materials with low energy electronic excitation spectrum similar to the massless two favour 3+1 Dirac fermions. The interaction between quasiparticles in Dirac semimetals is instantaneous Coulomb with large effective coupling constant α ∼ 1. In this report we present results of study of the phase diagram of Dirac semimetals within lattice simulation with rooted staggered fermions. In particular, we calculate the chiral condensate as a function of effective coupling constant and Fermi velocity anisotropy and thus determine the position of semimetal-insulator transition in Dirac semimetals.

Note on the Bloch theorem

“…Moreover, the interactions with the time delay complicate the system even more. As a result the direct analogue of the Bloch theorem in the QFT has not been established despite several attempts [7,[24][25][26][27][28].…”