Pairing and chiral spin density wave instabilities on the honeycomb lattice: A comparative quantum Monte Carlo study

Using finite-temperature determinantal quantum Monte Carlo calculations, we reexamine the pairing susceptibilities in the Hubbard model on the honeycomb lattice, focusing on doping levels onto and away from the Van Hove singularity (VHS) filling. For this purpose, electronic densities of 0.75 (at the hole-doping VHS) and 0.4 (well below the VHS) are considered in detail, where due to a severe sign problem at strong coupling strengths, we focus on the weak-interaction region of the Hubbard model Hamiltonian. By analyzing the temperature dependence of pairing susceptibilities in various symmetry channels, we find the singlet $d+id$ wave to be the dominant pairing channel both at and away from the VHS filling. We furthermore investigate the electronic susceptibility to a specific chiral spin density wave (SDW) order, which we find to be similarly relevant at the VHS, while it extenuates upon doping away from the VHS filling.

Figure 1

Rhombic honeycomb lattice geometry for $L=6$, with $N_s=72$ sites. Dashed lines enclose the two-site unit cells, and the bipartite sublattice structure is indicated by site-centered letters $A$ and $B$.

Figure 2

The average FT-DQMC sign, $\langle \mathrm{sign}\rangle$, for different lattice sizes as a function of (a) interaction strength $U$, (b) density $\rho$, and (c) temperature $T$.

Figure 3

Phases of the considered pairing channels along the corresponding directions on the honeycomb lattice: (a) NN extended $s$ wave, (b) NN $d+id$ wave, (c) NN $p+ip$ wave, (d) NNN $d+id$ wave, (e) NNN $p+ip$ wave, and (f) NNN $f$-wave.

Figure 4

Temperature dependence of the various pairing susceptibilities $P_{\alpha }$ for the noninteracting system ($U=0$), as obtained on an $L=6$ system for (a) $\rho =0.4$ and (b) $\rho =0.75$.

Figure 5

Temperature dependence of the effective pairing susceptibilities $P_{\alpha }^{\text{eff}}$ at density $\rho =0.4$ on the $L=6$ lattice for (a) $U/t=1$, (b) $U/t=2$, (c) $U/t=3$, and (d) $U/t=4$.

Figure 6

Temperature dependence of the effective pairing susceptibilities $P_{\alpha }^{\text{eff}}$ at density $\rho =0.4$ on the $L=12$ lattice for $U/t=2$.

Figure 7

Temperature dependence of the effective pairing susceptibilities at the VHS filling ($\rho =0.75$) on the $L=6$ lattice for (a) $U/t=1$ and (b) $U/t=2$.

Figure 8

Temperature dependence of the effective pairing susceptibilities at the VHS filling ($\rho =0.75$) on the $L=10,12$, and 14 lattices for (a) $U/t=1$ and (b) $U/t=2$.

Figure 9

Temperature dependence of the structure factor $S_{\mathrm{cSDW}}$ at $\rho =0.75$ and $\rho =0.4$ for (a) $U/t=1$ on the $L=6$ lattice and (b) $U/t=2$ for lattice sizes $L=6,10,12,14$.

Figure 10

Temperature dependence of ${\chi }_{\mathrm{cSDW}}^{}$ for $\rho =0.4$ and $\rho =0.75$ at $U/t=0$ on the $L=6$ lattice.

Figure 11

Temperature dependence of ${\chi }_{\mathrm{cSDW}}^{\text{eff}}$ at $\rho =0.4$ and $\rho =0.75$ for (a) $U/t=1$ on a $L=6$ lattice and (b) $U/t=2$ on $L=6,10,12$, and 14 lattices.

Figure 12

Structure factors $S_{\mathrm{cSDW}}$ and $S_{\mathrm{AF}}$ as functions of $\rho$ for several values of $U/t$ for $T/t=1/12$ on the $L=6$ lattice. For $U/t=2$, data for the $L=12$ lattice are also shown.

Figure 13

Effective susceptibilities ${\chi }_{\mathrm{cSDW}}^{\text{eff}}$ and ${\chi }_{\mathrm{AF}}^{\text{eff}}$ as functions of $\rho$ at $T/t=1/12$ for (a) $U/t=1$ on the $L=6$ lattice and (b) $U/t=2$ on both $L=6$ and $L=12$ lattices.

Figure 14

Electronic density $\rho$ as a function of the chemical potential $\mu$ on the $L=6$ and $L=12$ lattices for $U/t=2$ and $T/t=1/12$.