Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice

Understand

Using first-principle Hybrid-Monte-Carlo (HMC) simulations, we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in the extended Hubbard model on the two dimensional hexagonal lattice at half filling.

• We determine the phase diagram in the space of on-site and nearest-neighbor couplings $U$ and $V$ in the region $V<U/3$, which can be simulated without a fermion sign problem, and find that a transition from semimetal to a SDW phase occurs at sufficiently large $U$ for basically all $V$.
• Tracing the corresponding phase boundary from $V=0$ to the $V=U/3$ line, we find evidence for critical scaling in the Gross-Neveu universality class for the entire boundary.
• With rather high confidence we rule out the existence of the CDW ordered phase anywhere in the range of parameters considered.