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International Conference on Strongly Correlated Electron Systems (SCES)

Metallization of Mott Insulators through Percolation in Partially Filled Impurity Hubbard Model

Hisatoshi Yokoyama, Ryo Sato, Kenji Kobayashi, Tsutomu Watanabe, Masao Ogata

Published Mar 18, 2020• 0 citations
Publisher

Abstract

An impurity Hubbard model with strong correlation on a square lattice with diagonal hopping is studied for an antiferromagnetic state, using a variational Monte Carlo method.If the impurity potential is repulsive with moderate strength and the density of impurity sites is equal to or larger than the doping rate in a partially filled band, the state becomes insulating.When the impurity density is increased, an insulator-to-metal transition takes place through a mechanism of percolation.

DOI
10.7566/jpscp.30.011003

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An impurity Hubbard model with strong correlation on a square lattice with diagonal hopping is studied for an antiferromagnetic state, using a variational Monte Carlo method.If the impurity potential is repulsive with moderate strength and the density of impurity sites is equal to or larger than the doping rate in a partially filled band, the state becomes insulating.When the impurity density is increased, an insulator-to-metal transition takes place through a mechanism of percolation.
In view of cuprate superconductors, effects of point-type repulsive impurity potential ( V ) on partially filled antiferromagnetic (AF) states are studied for a strongly correlated square-lattice Hubbard model ( U/t = 12) with a diagonal transfer ( t ' = −0.3 t ), using a variational Monte Carlo method. To simplify interpretation, here we focus on the case of δ imp = δ, where δ imp and δ are densities of impurity sites and doped holes, respectively, with δ = 0.04 − 0.20. As a result, a filling-control-type Mott transition occurs at V = V M ( ∼ 2 t ) irrespective of δ ; a partially filled AF state becomes Mott insulating for V > V M . Such impurity-induced Mott transitions extensively appear beyond the above parameter settings.
Abstract In view of cuprate superconductors, effects of point-type impurity potential (V) on half-filled antiferromagnetic and paramagnetic states are studied for a strongly correlated square-lattice Hubbard model (U/t = 12) with a diagonal transfer (t′), using a variational Monte Carlo method. In the trial states, we introduce a Rice-Brinkman-type one-body projector for V, which enables us to treat the whole range of V (− ∞ < V/t < ∞) with small statistical errors. Filling-control-type Mott (insulator-to-metal) transitions are found to occur at <?CDATA V=VU(±)V=V_{U}^{\left( \pm \right)}V=VU(±)​?> V = V U ( ± ) (∼ ±U). In the metallic states <?CDATA (∣V∣>∣VU(±)∣)\left( \left| V \right|>\left| V_{U}^{\left( \pm \right)} \right| \right)(∣V∣>​VU(±)​​)?> ( | V | > | V U ( ± ) | ) , charge carriers are holes (electrons) in the case of attractive (repulsive) potential. The mechanism of the transitions is intuitively understood.
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U . With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
Abstract. We investigate the phase diagram of the square lattice bilayer Hubbard model at half filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping t ⊥ and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: An antiferromagnetic Mott insulator at small t ⊥ for any value of U and a band insulator at large t⊥. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t ⊥ a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing t ⊥ in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h 1.
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator transition.
Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account of the ground-state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite on-site repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonic finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.