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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

New formalism in evaluation of the ground and few excited states of Hubbard chain nanostructures

Edris Faizabadi, Maryam Soleimani

Published Nov 15, 2007• 0 citations
Publisher

Abstract

A new, simple and efficient method is presented for calculation of the ground and a few excited states of Hubbard chain nanostructures. By using this method, the photoemission spectral function for organic charge transfer salt TTF-TCNQ, is calculated. For a chain with maximum 70 sites the result is in good agreement with the previous works but there is a difference for further number of sites in the chain, which is discussed in the text with all the specifics. We also show that a source of errors in density matrix renormalization group method for a one dimensional chain is the deficiency of the matrix product scheme for generating the desired states of the linear chain.

DOI
10.1117/12.757917

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•Jan 1, 2025•0 citations
A new, simple and efficient method is presented for calculation of the ground and a few excited states of Hubbard chain nanostructures. By using this method, the photoemission spectral function for organic charge transfer salt TTF-TCNQ, is calculated. For a chain with maximum 70 sites the result is in good agreement with the previous works but there is a difference for further number of sites in the chain, which is discussed in the text with all the specifics. We also show that a source of errors in density matrix renormalization group method for a one dimensional chain is the deficiency of the matrix product scheme for generating the desired states of the linear chain.
We calculate the photoemission spectral function of the one-dimensional Hubbard model away from half filling using the dynamical density-matrix renormalization group method. An approach for calculating momentum-dependent quantities in finite open chains is presented. Comparison with exact Bethe ansatz results demonstrates the unprecedented accuracy of our method. Our results show that the photoemission spectrum of the quasi-one-dimensional conductor TTF-TCNQ provides evidence for spin-charge separation on the scale of the conduction bandwidth.
We present a method for the calculation of few-electron spectral functions of the one-dimensional Hubbard model which relies on a pseudofermion description introduced recently in Ref. [6]. The spectral functions are expressed as a convolution of pseudofermion dynamical correlation functions. Our general method involves the direct evaluation of the matrix elements of pseudofermion operators between the ground state and the excited states. We briefly discuss the application of our general method to the study of the unusual finite-energy spectral properties observed in the quasi-one-dimensional organic conductor TTF-TCNQ.
The Hubbard model is a simple but profound theoretical tool for understanding the physics underlying strongly correlated systems. This phenomenology includes, but is not limited to, metal-insulating transitions, charge and spin order (charge density/spin density waves), superconducting phases, non-Fermi liquid physics, among others. Examining one dimensional physical models described by the Hubbard Hamiltonian can teach us much about the related physics of higher dimensional systems. Applying advanced numerical computational techniques such as density matrix numerical renormalization group (DMRG) to one-dimensional manypbody model Hamiltonians allows for the calculation of ground state energies and dynamical spectral functions with extremely high precision and accuracy. This thesis explores the application of DMRG numerical techniques to one-dimensional physical systems described by Hamiltonians beyond the conventional Hubbard model, and the nuanced physical effects observed for these systems across various regimes and phases. A Wannier Hubbard chain composed of non-orthogonal overlapping atomic orbitals was transformed to an orthogonal atomic basis using a non-unitary Lowdin transformation. The calculation of energies, dynamical spectral functions and the photoemission spectrum for this Wannier Hubbard chain revealed phases not previously observed for Hubbard chains at half-filling. Additional analysis and calculations were performed for a CuO chain described by the Luther-Emery Hamiltonian that epitomizes charge-transfer physics. The motivation for studying this CuO chain was previous literature on transition metal oxides (TMOs) and the mapping of multiband Hamiltonians to single band models in certain energy regimes. Finally, we performed computational analysis for a spin-3/2 generalized Hubbard chain. By spanning the full phase space of our spin-3/2 Hubbard chain in terms of chemical potential μ\muμ and external magnetic field hhh we observed non-typical Cooper pairing states and novel phases for different symmetries of our Hamiltonian.--Author's abstract