Numerical evidence of conformal phase transition in graphene with long-range interactions

Abstract

Using state of the art 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 suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement. * Pavel.Buividovich@physik.uni-regensburg.de †

Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice

“…𝑈 𝑐 /𝜅 𝜈 β Grand canonical BRS HMC ([3], present work) 3.835 (14) 1.181(43) † 0.898(37) Grand canonical BSS HMC, complex AF [8] 3.90(5) 1.162 1.08(2) Grand canonical BSS QMC [12] 3.94 0.93 0.75 Projection BSS QMC [1] 3.85(2) 1.02(1) 0.76(2) Projection BSS QMC [13] 3.80(1) 0.84(4) 0.71(8) Projection BSS QMC, pinning field [10] 3.78 0.882 * 0.794 * GN 4 − 𝜖 expansion, 1st order [1,9] 0.882 * 0.794 * GN 4 − 𝜖 expansion, 1st order [1,11] 0.851 0.824 GN 4 − 𝜖 expansion, 2nd order [1,11] 1.01 0.995 GN 4 − 𝜖 expansion, 𝜈 2nd order [4,11] 1.08 1.06 GN 4 − 𝜖 expansion, 1/𝜈 2nd order [4,11] 1.20 1.17 GN FRG [4] 1.31 1.32 GN FRG [14] 1.26 GN Large 𝑁 [15] 1.1823 the discrepancy between expansions for 𝜈 and 1/𝜈 persists. Finally, our critical exponent β does not agree with any results previously derived in the literature.…”

Density of states approach to the hexagonal Hubbard model at finite density

“…We carried out LLR calculations for a fixed temperature of β ¼ 2.7κ −1 , two different lattice sizes (6 3 and 12 3 ) and different interaction strengths in the weak and intermediate coupling regime, and obtained the particle density as a function of chemical potential. We thereby observed significant deviations from the noninteracting theory for the largest interaction strength considered, U=κ ¼ 2.0, signaling strong correlations which might eventually lead to spontaneous mass-gap formation which is known to occur at around U=κ ≈ 3.8 [12,34] in the infinite-volume limit.…”

“…using Hybrid Monte Carlo by now have a long history [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]; we thus summarize only the essential steps here. 1 To derive the functional integral representation of the partition function at inverse temperature β ¼ 1=T, we first write the exponential in terms of N t identical factors and split the Hamiltonian into the free tight-binding part plus interactions,Ĥ ¼Ĥ 0 þĤ int .…”

Mitigating spikes in fermion Monte Carlo methods by reshuffling measurements

“…P (x 1 , x 2 ) includes the Gaussian part and the remaining terms model fermion determinants. This structure is inspired by the Hubbard-Stratonovich decomposition with continuous auxiliary fields routinely employed in determinantal QMC [6,14,15] (see section III below for the detailed explanation). Our toy "determinants" are equal to zero along the lines x 1 = f (x 2 ) and x 2 = f (x 1 ), and we need the second power of each multiplier since there are two equivalent fermion determinants for electrons and holes on a bipartite lattice at half-filling.…”