We reinterpret the Hubbard model in terms of doubly occupied sites and empty sites with an attractive interaction U whose pairing leads to the Mott-Hubbard transition. We develop a mean-field theory for this pairing which in a triangular lattice at T=0 leads to a first-order transition from a spiral, incommensurate metal to a commensurate insulator at U\ensuremath{\simeq}5.27t where a charge gap (\ensuremath{\simeq}0.085t) opens up. We also discuss the effect of fluctuations.
We reinterpret the Hubbard model in terms of doubly occupied sites and empty sites with an attractive interaction U whose pairing leads to the Mott-Hubbard transition. We develop a mean-field theory for this pairing which in a triangular lattice at T=0 leads to a first-order transition from a spiral, incommensurate metal to a commensurate insulator at U\ensuremath{\simeq}5.27t where a charge gap (\ensuremath{\simeq}0.085t) opens up. We also discuss the effect of fluctuations.
We investigate the metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number z that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in 1/z and becomes exact on the infinite-z Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard Uc and the corresponding doublon density ndc, hopping ${\ensuremath{\chi}}_{d}^{c}$ and doublon-holon pairing ${\mathrm{\ensuremath{\Delta}}}_{d}^{c}$ amplitudes. We find ${U}_{c}={U}_{\mathrm{BR}}[1\ensuremath{-}2{n}_{d}^{c}\ensuremath{-}\sqrt{z}({\ensuremath{\chi}}_{d}^{c}+{\mathrm{\ensuremath{\Delta}}}_{d}^{c})]\ensuremath{\simeq}0.8{U}_{\mathrm{BR}}$, where UBR is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a U(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-z limit and lifts the 2N-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact U(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.
Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at Uc∼7.4t , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.
We investigate a nonmagnetic metal-insulator transition in the 1/5-depleted square lattice Hubbard model at half filling within the eight-site cellular dynamical mean field theory. We find that a metal-insulator transition without any signatures of a first-order transition, a continuous Mott transition, takes place in a certain range of parameters. The nature of the continuous Mott transition is merely a Lifshitz transition driven by the on-site Coulomb interaction. The renormalized matrix elements of hoppings and the spin-spin correlation functions reveal that the physics of this transition is a strong enhancement of the dimerization due to the nonlocal effects of the electron-electron interaction.
We study the metal-insulator transition and magnetic ordering in the Hubbard model using the particle-hole mapping. This representation facilitates the exact solution of the half-filled band in the limit of high spin. We find that the two-dimensional Hubbard model has a charge-excitation gap at half filling for any finite U in the high-spin region on both the bipartite square lattice and the nonbipartite triangular lattice. We show, using the Kohn insulator criteria, that this bound-state phase is indeed insulating. Using the information from the single-pair solution, we construct a generalized BCS type of many-body wave function and derive the gap equation for lower-spin states. We find that in some cases, the system goes through a phase transition to become a metal as the total spin Sz is lowered.
We study two-component fermions in optical lattices with spatially alternating on-site interactions using dynamical mean-field theory. Calculating the quasi-particle weight, double occupancy, and order parameters for each sublattice, we discuss the low-temperature properties of the system. When both interactions are repulsive, the magnetically ordered state is realized at half-filling. In the attractive case, the superfluid state is, in general, realized with a particle number imbalance. On the other hand, when repulsive and attractive interactions are comparable in the half-filled system, the magnetically ordered and superfluid states are not realized, but the metal-insulator transition occurs. This transition is characterized by the Mott and pairing transitions discussed in the conventional repulsive and attractive Hubbard models. In the doped system, commensurability emerges owing to the repulsive interactions and the metal-insulator transition occurs down to quarter-filling.