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arXiv:cond-mat/0604609 · Physical Review B

Dynamical mean-field study of the Mott transition in the half-filled Hubbard model on a triangular lattice

Karan Aryanpour, Warren E. Pickett, Richard T. Scalettar

Published Aug 30, 2006• 54 citations
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Abstract

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.

DOI
10.1103/physrevb.74.085117

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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 Uc=12.0\ifmmode±\else\textpm\fi0.5{U}_{c}=12.0\ifmmode\pm\else\textpm\fi{}0.5Uc​=12.0\ifmmode±\else\textpm\fi0.5 in units of the hopping amplitude ttt through the evolution of the magnetic moment, spectral function, internal energy, and specific heat as the interaction UUU and temperature TTT 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.
We present clear numerical evidence for the coexistence of metallic and insulating dynamical mean-field theory (DMFT) solutions in a half-filled single-band Hubbard model at finite temperature. The quantum Monte Carlo (QMC) method is used to solve the DMFT equation. We discuss important technical aspects of the DMFT-QMC method, which should be properly dealt with in order to obtain reliable DMFT solutions at low temperatures. Among these technical aspects are the critical slowing down near the boundaries of the coexistence region, the convergence criteria for the DMFT iterations, and the correct interpolation of the discretized Green's functions.
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 Pad\'e 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.
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)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​) in the temperature-interaction plane T−UT-UT−U. A number of crossovers occur along lines that extend for some range above (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​). Asymptotically close to (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​), these lines coalesce into the so-called Widom line. The existence of (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​) and of the associated crossovers becomes unclear when long-wavelength fluctuations or long-range order occur above (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(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".
The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous-time auxiliary-field quantum Monte Carlo to solve this model for 1-, 4-, 6-, 12-, and 16-site clusters with detailed analysis performed for the 6-site cluster. We show that (a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; (b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; and (c) the loss of spectral weight in the metal-to-Mott-insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.
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.
We study the Mott transition in the two dimensional Hubbard model by using the variational cluster approximation. The transition potential obtained is roughly Uc ≈ 2 and 6 for square and triangular lattices, respectively. A comparison between results of this approximation and other quantum cluster methods is presented. Our zero-temperature calculation at strong coupling show that the transition on the triangular and square lattices occur at lower values of compared with other numerical techniques such as DMFT, CDMFT, and DCA. We also study the thermodynamic limit by an extrapolation to infinite size.