We employ dynamical mean-field theory (DMFT) with a quantum Monte Carlo atomic solver to investigate the finite-temperature Mott transition in the Hubbard model with nearest-neighbor hopping on a triangular lattice at half-filling. We estimate the value of the critical interaction to be ${U}_{c}=12.0\ifmmode\pm\else\textpm\fi{}0.5$ in units of the hopping amplitude
t through the evolution of the magnetic moment, spectral function, internal energy, and specific heat as the interaction
U and temperature
T are varied. This work also presents a comparison between DMFT and finite-size determinant quantum Monte Carlo calculations and a discussion of the advantages and limitations of both methods.
The interaction-driven Mott transition in the half-filled Hubbard model is a first-order phase transition that terminates at a critical point
(Tc,Uc) in the temperature-interaction plane
T−U. A number of crossovers occur along lines that extend for some range above
(Tc,Uc). Asymptotically close to
(Tc,Uc), these lines coalesce into the so-called Widom line. The existence of
(Tc,Uc) and of the associated crossovers becomes unclear when long-wavelength fluctuations or long-range order occur above
(Tc,Uc). We study this problem using continuous-time quantum Monte Carlo methods as impurity solvers for both Dynamical Mean-Field Theory (DMFT) and Cellular Dynamical Mean-Field Theory (CDMFT). We contrast the cases of the square lattice, where antiferromagnetic fluctuations dominate in the vicinity of the Mott transition, and the triangular lattice where they do not. The inflexion points and maxima found near the Widom line for the square lattice can serve as proxy for the triangular lattice case. But the only crossover observable in all cases at sufficiently high temperature is that associated with the opening of the Mott gap. The same physics also controls an analog crossover in the resistivity called the "Quantum Widom line".
We investigate the Mott metal-insulator transition in the asymmetric Hubbard model, which may describe the ground states of fermionic atoms trapped in optical lattices. We use the dynamical mean-field theory and the equation of motion approach to calculate the density of states at the Fermi level and the double occupation for various values of the on-site interaction U and the hopping asymmetry r . The critical interaction is also obtained as a function of the hopping asymmetry. Our results are in good agreement with the ones obtained by using the dynamical mean field theory with the exact diagonalization and the quantum Monte Carlo techniques.