The thermodynamical limit of strongly correlated systems obtained from small-size-cluster calculations

Chiappe, G.; Büsser, C. A.; Anda, E. V.; Ferrari, V.

doi:10.1088/0953-8984/11/27/301

Cited by 3 publications

(2 citation statements)

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“…10,11,12,13 Ideas similar to the embedded cluster method have been applied to the metal-insulator transition of the Hubbard model. 14,15,16 Incorporating ideas from the Density Matrix Renormalization Group method (DMRG) 17 into NRG and vice versa has also resulted in substantial improvements in, e.g., the calculation of dynamical properties 18 or time-evolution schemes, 19 which now allows one to address problems previously out of reach for either method. In the same spirit, it is the objective of this paper to present the Logarithmic Discretization Em-bedded Cluster Approximation (LDECA) approach to study highly correlated electrons in nano-scale systems, combining ECA with Wilson's idea of a logarithmic discretization of the conduction band.…”

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confidence: 99%

Method to study highly correlated nanostructures: The logarithmic-discretization embedded-cluster approximation

et al. 2008

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This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.

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Section: Introductionmentioning

confidence: 99%

Method to study highly correlated nanostructures: The logarithmic-discretization embedded-cluster approximation

et al. 2008

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“…In zigzag honeycomb ribbons, VCA has been applied to study the transition from topological to antiferromagnetic insulators [32]. CPT shares the strategy of cluster embedding with other approaches that have been developed to study transport in nanoscopic structures [33][34][35][36] or the metal-insulator transition of the Hubbard model [37].…”

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Reentrant metallicity in the Hubbard model: the case of honeycomb nanoribbons

Manghi¹,

Petocchi²

2014

Phys. Scr.

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Based on the Cluster Perturbation solution of the Hubbard hamiltonian for a 2-D honeycomb lattice we present quasiparticle band structures of nanoribbons at half filling as a function of the on-site electron-electron repulsion. We show that at moderate values of e-e interaction ribbons with armachair shaped edges exhibit an unexpected semimetallic behavior, recovering the original insulating character only at larger values of U .The repulsive interaction among electrons is responsible of the failure of single particle picture and of the opening/widening of energy gaps in solids. The Hubbard model is the paradigm to describe this phenomenon: sufficiently large values of the on-site e-e repulsion inhibit the inter-site hopping favoring in this way an insulating behaviour. The 1-atom thick 2D honeycomb lattice (graphene) does not contradict this picture: many body effects due to on-site Coulomb repulsion have been shown to lead, for sufficiently strong interactions, to semimetalto-insulator transition 1,2 as well as to other deviations from Fermi-liquid behavior such as unconventional quasiparticle lifetimes 3 , long range antiferromagnetic order 4 and spin liquid phase 5 .In this paper we show that for honeycomb nanoribbons the repulsive e-e interaction may be responsible of a metallic phase in ribbons that in the single particle picture are semiconducting. This appears to be another extraordinary property of the 2-D honeycomb lattice.It is well known that honeycomb nanoribbons manifest peculiar properties related to the topology of their edges 6 : according to single-particle theory ribbons with armchair shaped edges may exhibit a finite energy gap depending on their width 7-9 , while ribbons with zigzag edges are metallic and become insulating only after the inclusion of an antiferromagnetic order 10,11 . The modifications of the single particle band structure of zigzag graphene ribbons due to e-e interaction has been investigated within a mean field solution of the Hubbard model 12,13 , showing spin polarization of edge states and gap opening at the Fermi level. How the single particle band picture evolves to a quasi-particle one and how the electronic states of both armchair and zigzag honeycomb ribbons are modified by on-site Coulomb repulsion described as a true many body term is the question we address in this paper.We have adopted a many body approach based on the Cluster Perturbation Theory 14 (CPT). CPT belongs to the class of Quantum Cluster theories 15 that solve the problem of many interacting electrons in an extended lattice by a divide-and-conquer strategy, namely solving first the many body problem in a subsystem of finite size and then embedding it within the infinite medium.Quantum Cluster theories represent some of the most powerful tools for the numerical investigation of strongly correlated many-body systems. They include Dynamical Cluster Approach 16 , Cellular Dynamical Mean Field Theory 17 as well as CPT and have found an unified language within the variational scheme 18 based on the the Sel...

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