Hubbard model on the triangular lattice using dynamical cluster approximation and dual fermion methods

We investigate the Hubbard model on the triangular lattice at half filling using the dynamical cluster approximation (DCA) and dual fermion (DF) methods in combination with continuous-time quantum Monte Carlo (CT QMC) and semiclassical approximation (SCA) methods. We study the one-particle properties and nearest-neighbor spin correlations using the DCA method. We calculate the spectral functions using the CT QMC and SCA methods. The spectral function in the SCA and obtained by analytic continuation of the Padé approximation in CT QMC are in good agreement. We determine the metal-insulator transition and the hysteresis associated with a first-order transition in the double-occupancy and nearest-neighbor spin-correlation functions as functions of temperature. As a further check, we employ the DF method and discuss the advantages and limitation of the dynamical mean-field theory, DCA, and recently developed DF methods by comparing the Green’s functions. We find an enhancement of antiferromagnetic correlations and provide evidence for magnetically ordered phases by calculating the spin susceptibility.

Figure 1

(a) Schematic representation of triangular lattice with electron hoppings. (b) Equivalent representation of (a) for a square structure. (c) Example of the coarse-graining cells in the BZ for the triangular lattice (a) where the cluster size is $N_c=4$.

Figure 2

One-particle spectral function $A\left(K,\omega \right)$ corresponding to the $K=\left(\pi ,\pi /\sqrt{3}\right)$ for $\beta =1.6667$, (a) $U=6$, and (b) $U=9$ by means of the SCA and CT QMC with Padé approximation.

Figure 3

Total DOS with $N_c=4$ and 16 for $\beta =4$, (a) $U=6$, and (b) $U=10$ via CT QMC with Padé approximation.

Figure 4

Double occupancy as a function of $U/t$ at several temperatures for $N_c=4$. $U_c=7.2$ for $T=0.2$, $U_c=6.9$ for $T=0.1$, and $U_c=6.7$ for $T=0.05$.

Figure 5

The nearest-neighbor spin-correlation function as a function of $U/t$ at several temperatures for $N_c=4$. $U_c=7.2$ for $T=0.2$, $U_c=6.9$ for $T=0.1$, and $U_c=6.7$ for $T=0.05$.

Figure 6

(Color online) The imaginary part of the on-site Green’s function for $\beta =4$, (a) $U=6$, and (b) $U=10$. The real part of the nearest-neighbor Green’s function for $\beta =4$, (c) $U=6$, and (d) $U=10$.

Figure 7

(Color online) (a) The spin susceptibility $\chi \left(q\right)$ in the insulating state for $U/t=10.0$ and $\beta t=2.5$. (b) The spin susceptibility as a function of temperature at $q=\left(0,0\right)$ and $\left(2\pi /3,2\pi /3\right)$.