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

Abstract

We employ dynamical mean field theory (DMFT) with a Quantum Monte Carlo (QMC) atomic solver to investigate the finite temperature Mott transition in the Hubbard model with the nearest neighbor hopping on a triangular lattice at half-filling. We estimate the value of the critical interaction to be Uc = 12.0 ± 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 (DQMC) and a discussion of the advantages and limitations of both methods.PACS numbers: I. MOTIVATIONSystems with triangular lattice structure have been a source of attention mostly due to the frustration effects resulting from their non-bipartite structure. As a result of the competition between the frustration and strong electron correlations, these systems exhibit a wide range of exotic phases. Recent studies of the metalinsulator transition, superconductivity, and antiferromagnetism in the organic compounds κ-(BEDT-TTF) 2 X with X as an anion 1,2 , discovery of superconductivity in Na x CoO 2 .yH 2 O, 3 and the recent discovery of the Mott transitions in 0.33 monolayers of Sn on Ge(111) at 30 K, 4 as a few examples, underline the importance of these systems and their physics.Theoretical work has been dedicated to the discovery of the magnetically ordered phases in the ground state of the Hubbard and t − J models on triangular lattices as a function of the on-site electron-electron Coulomb interaction U at different fillings. 5,6,7,8,9,10 Unlike the square lattice at half-filling, which is a Mott insulator with antiferromagnetic order at arbitrarily small values of U/t, the ground state of a triangular lattice has a variety of magnetically ordered and disordered phases. This is due to the lack of perfect nesting in the non-interacting Fermi surface of a triangular lattice at half-filling.For triangular lattices, according to the Hartree-Fock calculations of Krishnamurthy and co-workers, 5,6 the Mott transition occurs from a paramagnetic metal to a paramagnetic insulator at half-filling for values of U larger than the band width W = 9t. A variety of the physical properties of the triangular lattices including tendencies towards superconductivity within the small to intermediate U regime have been studied at finite temperature using correlated electron approaches which go beyond mean field theory, such as the fluctuation exchange approximation (FLEX) 11 or one-loop renormalization-group. 12 However, when U/W ≥ 1, a more powerful cluster solving technique such as the Quantum Monte Carlo (QMC) is required to accurately describe the phase transition. Finite size lattice determi-nant Quantum Monte Carlo (DQMC) has already been employed for triangular and kagomé lattices. 13,14 Unfortunately, the finite size lattice QMC method incurs sign problems at both low temperatures and away from halffilling. In addition, due to the finite s...

Mott transition in two-dimensional frustrated compounds

“…Here, U c2 Ϸ 1 / 2.63 eVϷ 9.5t, whereas U c2 Ϸ 12t -15t in local DMFT for the triangular lattice. 35,36 Comparing Figs. 1͑a͒ and 1͑b͒, it is evident that anisotropy causes a further lowering of the critical Coulomb energies.…”

Imaginary-time quantum many-body theory out of equilibrium. II. Analytic continuation of dynamic observables and transport properties

“…A common way to deal with this problem is the so-called "annealing procedure". 28,29 Here, a fine temperature grid is imposed in order to freeze out low-energy features step by step. The procedure starts with a featureless default model at very high temperatures.…”

Competition between charge and spin order in thet−U−Vextended Hubbard model on the triangular lattice

“…With help of this calculation and also of NMR experiments 7 , one can find a rough estimate of hopping and exchange constants that would enter a two-dimensional Hubbard or t − J model for this system. However, the modeling is complicated by the fact that band structure calculations lead to hole pockets that are not observed experimentally, a question that is still debated by several groups using, for example, the Gutzwiller approximation 15 , the local density approximation plus Hubbard 16 U and dynamical-mean field theory 17,18,19 . In addition, the effect of long-range Coulomb interaction from the sodium leads to modifications to the simplest Hubbard Hamiltonian for the cobaltates 20,21 .…”