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International Journal of Quantum Chemistry

Metal–insulator transition in the Hubbard model on a triangular lattice with disorders: Renormalization group approach

J. X. Wang, Sabre Kais

Published Jan 1, 2003• 3 citations
Publisher

Abstract

Abstract A multistages block renormalization group approach to study the metal–insulator transition in the Hubbard model on a triangular lattice with hexagonal blocks is presented and implemented. A second‐order phase transition with a critical point at U/t = 12.5 is obtained (the coupling parameters U and t correspond to the repulsive charging energy and to the nearest‐neighbor exchange coupling terms, respectively). In the presence of disorder the phase diagram for the system exhibits a metallic phase, an insulating phase, and a domain‐localized phase that separates them in the Mott regime. The subtle influence of electron–electron interactions upon inverse participation rate in the Anderson regime is also investigated. The results are discussed in light of experimental evidence for arrays of metalic quantum dots and exact numerical diagonalization of the Hubbard Hamiltonian. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 360–374, 2003

DOI
10.1002/qua.10572

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Abstract A multistages block renormalization group approach to study the metal–insulator transition in the Hubbard model on a triangular lattice with hexagonal blocks is presented and implemented. A second‐order phase transition with a critical point at U/t = 12.5 is obtained (the coupling parameters U and t correspond to the repulsive charging energy and to the nearest‐neighbor exchange coupling terms, respectively). In the presence of disorder the phase diagram for the system exhibits a metallic phase, an insulating phase, and a domain‐localized phase that separates them in the Mott regime. The subtle influence of electron–electron interactions upon inverse participation rate in the Anderson regime is also investigated. The results are discussed in light of experimental evidence for arrays of metalic quantum dots and exact numerical diagonalization of the Hubbard Hamiltonian. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 360–374, 2003
In this paper, we have investigated the metal-insulator transition (MIT) in a two-dimensional half-filled extended Hubbard model on an isotropic triangular lattice with a real space block renormalization group technique. It has been found that the MIT can be driven nontrivially by either the on-site interaction U or the nearest-neighbor one V, but with different critical exponents. Depending upon the values of V, the system could have one, two or three MIT critical points. Moreover, for the metallic regime, we have also studied the competition effect from the spin density wave and charge density wave phases by using a mean-field theory based upon Hartree-Fock approximations. Finally, the single-site entanglement is also calculated and its first derivative with respect to U shows a jump along the critical line of the MIT.
We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.
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∼7.4tU_{\rm c} \sim 7.4tUc​∼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 study the quantum phase transition from an insulator to a metal realized at t'=t'_c > 0.5t in the ground state of the half-filled Hubbard chain with both nearest-neighbor (t) and next-nearest-neighbor (t') hopping. The study is carried out using the bosonization approach and density matrix renormalization group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well-described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line t'_c(U,t). We argue that close to the insulator-metal transition line, a crossover to a regime corresponding to an infinite-order transition takes place.We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.
Abstract Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.