2014/02/28 by Lukas Janssen, Igor F. Herbut · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1103/physrevb.89.205403
published as Phys. Rev. B 89, 205403 (2014) · 15 pages, 5 figures, 2 tables; v3: misprint in Eqs. (25) and (30) corrected, results unchanged
arxiv created 2020/11/30 · arxiv updated 2020/12/01
Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of on-site Hubbard repulsion. We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3) order parameter ("chiral Heisenberg universality class"). Our calculation yields an estimate of the critical exponents ν≃ 1.31, ηϕ≃ 1.01, and ηΨ≃ 0.08, in reasonable agreement with the second-order expansion around the upper critical dimension. To test the validity of the present method we use the conventional Gross-Neveu-Yukawa theory with Z(2) order parameter ("chiral Ising universality class") as a benchmark system. We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension. Directly in 2+1 dimensions, our chiral-Ising results agree with the best available predictions from other methods within the single-digit percent range for ν and ηϕ and the double-digit percent range for ηΨ. While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant. Discussion and summary of various approaches is presented.