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physica status solidi (b)

Few particles correlation in a one‐dimensional quasiperiodic lattice

J.R. Suárez, Emmanuel Vallejo, Eliel Carvajal, Oracio Navarro

Published Jun 13, 2005• 1 citation
Publisher

Abstract

Abstract During the last two decades, two of the most important discoveries in condensed matter physics have been the discovery of quasicrystals and the discovery of high‐Tc ceramic superconductors. These topics have generated a large number of experimental and theoretical studies in the physics of low dimension. They have also modified some of the concepts in solid state physics. For instance, it was believed that the five‐fold symmetry was incompatible with a long‐range order and it was not expected that ceramic materials with a high‐Tc and a short coherence length exhibit superconductivity. Therefore, it is important to revise both the spatial symmetry and the electronic correlation to identify how they affect the physical properties of materials. The study of these subjects is complex since we cannot use the reciprocal space to study quasicrystals and the electronic correlation in many‐body systems has not entirely been solved. Even in one‐dimensional quasiperiodic structures, the interactions between electrons have often been neglected and only few results have been obtained. In this work, we solved the cases of two and three interacting particles in a Fibonacci lattice using a real‐space method, the Green function technique, the renormalized perturbation expansion method and the Hubbard model. For the case of two interacting particles an analytical solution for the pairing phase diagram was obtained using the extended Hubbard Hamiltonian. For the case of three interacting particles the binding energy was numerically calculated. The results present here are compared with those obtained for the periodic and binary lattices. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200461780

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Abstract During the last two decades, two of the most important discoveries in condensed matter physics have been the discovery of quasicrystals and the discovery of high‐Tc ceramic superconductors. These topics have generated a large number of experimental and theoretical studies in the physics of low dimension. They have also modified some of the concepts in solid state physics. For instance, it was believed that the five‐fold symmetry was incompatible with a long‐range order and it was not expected that ceramic materials with a high‐Tc and a short coherence length exhibit superconductivity. Therefore, it is important to revise both the spatial symmetry and the electronic correlation to identify how they affect the physical properties of materials. The study of these subjects is complex since we cannot use the reciprocal space to study quasicrystals and the electronic correlation in many‐body systems has not entirely been solved. Even in one‐dimensional quasiperiodic structures, the interactions between electrons have often been neglected and only few results have been obtained. In this work, we solved the cases of two and three interacting particles in a Fibonacci lattice using a real‐space method, the Green function technique, the renormalized perturbation expansion method and the Hubbard model. For the case of two interacting particles an analytical solution for the pairing phase diagram was obtained using the extended Hubbard Hamiltonian. For the case of three interacting particles the binding energy was numerically calculated. The results present here are compared with those obtained for the periodic and binary lattices. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In this work we analyzed the ground-state symmetry for the cases of two particles in a linear Fibonacci chain, using the generalized Hubbard Hamiltonian and a previously developed real-space mapping method. The method is based on mapping the correlated many-body problem onto an equivalent site-and bond-impurity one-body problem in a higher dimensional space, where the problem can be solved exactly. For the case of two particles, it is obtained a ground-state when the correlated hopping interactions are included. The two particle problem is analyzed by looking at the phase diagram for the bound state. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
In this work we solve a general Hubbard Hamiltonian for two interacting particles in a periodic and nonperiodic infinite one-dimensional lattice, using a real-space mapping method, the renormalized perturbation expansion (RPE), and the Green-function technique. This Hamiltonian considers a general bond-charge interaction, the on-site interaction, and the general intersite interaction. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding problem in a higher-dimensional space. Analyzing the periodic and the quasiperiodic lattices in this new space, we obtained the analytical solution for the binding condition at the ground state. Our general results for the periodic chain reproduce completely the limit cases of the numerical solution obtained previously and those obtained in reciprocal space
Abstract Quantum dynamics in strongly correlated systems are of high current interest in many fields including dense plasmas, nuclear matter and condensed matter and ultracold atoms. An important model case are fermions in lattice systems that is well suited to analyze, in detail, a variety of electronic and magnetic properties of strongly correlated solids. Such systems have recently been reproduced with fermionic atoms in optical lattices which allow for a very accurate experimental analysis of the dynamics and of transport processes such as diffusion. The theoretical analysis of such systems far from equilibrium is very challenging since quantum and spin effects as well as correlations have to be treated non‐perturbatively. The only accurate method that has been successful so far are density matrix renormalization group (DMRG) simulations. However, these simulations are presently limited to one‐dimensional (1D) systems and short times. Extension of quantum dynamics simulations to two and three dimensions is commonly viewed as one of the major challenges in this field. Recently we have reported a breakthrough in this area [N. Schlünzen et al., Phys. Rev. B (2016)] where we were able to simulate the expansion dynamics of strongly correlated fermions in a Hubbard lattice following a quench of the confinement potential in 1D, 2D and 3D. The results not only exhibited excellent agreement with the experimental data but, in addition, revealed new features of the short‐time dynamics where correlations and entanglement are being build up. The method used in this work are nonequilibrium Green functions (NEGF) which are found to be very powerful in the treatment of fermionic lattice systems filling the gap presently left open by DMRG in 2D and 3D. In this paper we present a detailed introduction in the NEGF approach and its application to inhomogeneous Hubbard clusters. In detail we discuss the proper strong coupling approximation which is given by T ‐matrix selfenergies that sum up two‐particle scattering processes to infinite order. The efficient numerical implemen‐tation of the method is discussed in detail as it has allowed us to achieve dramatic performance gains. This has been the basis for the treatment of more than 100 particles over large time intervals. The numerical results presented in this paper concentrate on the diffusion in 1D to 3D lattices. We find that the expansion dynamics consist of three different phases that are linked with the build‐up of correlations. In the long time limit, a universal scaling with the particle number is revealed. By extrapolating the expansion velocities to the macroscopic limit, the obtained results show excellent agreement with recent experiments on ultracold fermions in optical lattices. Moreover we present results for the site‐resolved behavior of correlations and entanglement that can be directly compared with experiments using the recently developed atomic microscope technique. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The properties of a dilute electron gas, coupled to the lattice degrees of freedom, are studied and compared with the properties of an electron gas at half-filling, where spinless fermions with two orbitals per lattice site are considered. The simplest model which includes both the local electron-lattice interaction of the Jahn-Teller type and the electronic correlations is the E ⊗ β-Jahn-Teller-Hubbard model. We analyze the formation and stability of Jahn-Teller polarons and bipolarons, respectively. Our approach is based on a hopping expansion in the strong-coupling regime. The results are compared with recently published findings for the Hubbard-Holstein model [1, 2]. The special case of the Jahn-Teller-Hubbard model at half-filling is mapped on a spin-1/2 Heisenberg model with phonon-dependent coupling constants. This has been derived within a projection formalism that provides a continued-fraction representation of the Green's function. We study the exact solution for two and three particles and compare it with the effective theory on the infinite lattice with one particle per site. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract Our understanding of the physical properties of quantum many‐particle systems relies normally on the identification of elementary excitations that can be considered as weakly interacting building blocks of the whole system. In systems characterized by the presence of strong interactions between the elementary components, like high‐temperature superconductors and related materials or like ultra‐cold atoms in optical lattices, well known theoretical techniques like mean‐field or perturbation theories fail. On the contrary, quantum Monte Carlo simulations allow to handle such systems in a “numerically exact” way. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract The interplay and competition of magnetic and superconducting correlations in the weakly interacting two‐dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of interactions in one‐loop approximation evolves into a strong coupling regime at low energy scales, signalling the possible onset of spontaneous symmetry breaking. This is further analyzed by a mean‐field treatment of the strong renormalized interactions which takes into account magnetic and superconducting order simultaneously. The effect of strong correlations on single‐particle properties in the normal phase is studied by calculating the flow of the self‐energy. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)