In this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm.In this dissertation we report on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We demonstrate that the LRM is a viable method for investigating many body problems. For the Falicov-Kimball, an exact calculation of the atomic limit shows no sharp metal-insulator transition. A truncation approximation for the full hamiltonian has a smooth evolution from the atomic limit with the opening of a band for the conduction electrons. No phase transition was observed. A bose space calculation using the proper boson norm indicates that the conduction band induces a correlation between localized electrons on nearest-neighbor sites. It is not known if this effect is real or a by-product of the approximation. We applied the LRM to the Anderson Lattice and several of its limiting cases. In the limit of no hybridization, for both the symmetric and asymmetric (mixed-valence) parameter sets, we found that the thermodynamics could be described as competition between closely-lying energy levels. The effects that dominate are those that minimize the thermal average of the hamiltonian. A simple model is presented in which only hybridization between two localized orbitals is allowed. It shows that hybridization can give rise to mixed valence phenomena as the temperature approaches zero. For the full Anderson Lattice hybridization causes relatively small shifts in the occupation numbers of the localized and conduction electrons. However, these shifts can have dramatic effects on the physical properties as demonstrated by the magnetic susceptibilities. Band structures of the eigenenergies of the Liouville operator, for both parameter sets, reveal that low-lying excitations associated with some of the basis vector operators may split out from the fermi level and become significant at low temperatures. In addition, we report on progress toward extending the calculation to bose space using a commutator norm.

Jan 1, 19860 citations

Quasiparticles in Anderson Insulators : a Scenario of Delocalization induced by Interactions

Philippe Jacquod

APSMar 1, 19980 citations

Spectral properties of a narrow-band Anderson model

Steffen Schäfer, David E. Logan

We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth D is small compared to the hybridization strength ${\ensuremath{\Delta}}_{0}.$ Simple second-order perturbation theory (2PT) in U is found to produce a rich spectral structure that leads to rather good agreement with extant Lanczos results and offers a transparent picture of the underlying physics. It also leads naturally to two distinct regimes of spectral behavior, ${\ensuremath{\Delta}}_{0}Z/D\ensuremath{\gg}1$ and \ensuremath{\ll}1 (with Z the quasiparticle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ${\ensuremath{\Sigma}}_{i}(\ensuremath{\omega})$ is also examined beyond the confines of PT. It is argued that on frequency scales of order $\ensuremath{\omega}\ensuremath{\sim}\sqrt{{\ensuremath{\Delta}}_{0}D},$ the self-energy in strong coupling is given precisely by the 2PT result, and we point out that the resultant poles in ${\ensuremath{\Sigma}}_{i}(\ensuremath{\omega})$ connect continuously to that characteristic of the atomic limit. This in turn offers a natural rationale for the known inability of the skeleton expansion to capture such behavior, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in U.We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth D is small compared to the hybridization strength ${\ensuremath{\Delta}}_{0}.$ Simple second-order perturbation theory (2PT) in U is found to produce a rich spectral structure that leads to rather good agreement with extant Lanczos results and offers a transparent picture of the underlying physics. It also leads naturally to two distinct regimes of spectral behavior, ${\ensuremath{\Delta}}_{0}Z/D\ensuremath{\gg}1$ and \ensuremath{\ll}1 (with Z the quasiparticle weight), whose existence and essential characteristics are discussed and shown to be independent of 2PT itself. The self-energy ${\ensuremath{\Sigma}}_{i}(\ensuremath{\omega})$ is also examined beyond the confines of PT. It is argued that on frequency scales of order $\ensuremath{\omega}\ensuremath{\sim}\sqrt{{\ensuremath{\Delta}}_{0}D},$ the self-energy in strong coupling is given precisely by the 2PT result, and we point out that the resultant poles in ${\ensuremath{\Sigma}}_{i}(\ensuremath{\omega})$ connect continuously to that characteristic of the atomic limit. This in turn offers a natural rationale for the known inability of the skeleton expansion to capture such behavior, and points to the intrinsic dangers of partial infinite-order summations that are based on PT in U.

arXiv:cond-mat/0011216Physical review. B, Condensed matterJan 9, 20014 citations

Charge gaps and quasiparticle bands of the ionic Hubbard model

T. Jabben, N. Grewe, Frithjof B. Anders

arXiv:cond-mat/0502560The European Physical Journal BMar 1, 200514 citations

Quasiparticle picture for high-harmonic generation in correlated electron systems

Kai Huang, Tao-Yuan Du

The key optical and electronic functionalities in condensed materials are determined by the band filling of electrons and their Coulomb correlations. To directly capture how many-body correlations influence the correlated electron dynamics under the driving of laser pulses, the comprehensible quasiparticle picture is desired to distinguish the ultrafast creation and annihilation of doublon-holon pairs in attosecond timescale. Here, we adopt the one-dimensional non-half-filling Hubbard model to study the high-harmonic generation (HHG) in correlated electron systems. As the value of Hubbard $U$ increases, the cutoff energy and spectral features in HHG spectra have been revealed and their scaling laws are explained by the characteristic energy gaps obtained from the electronic bands under the quasiparticle picture. The adjustable degree of band filling in correlated systems paves a way to enhance high-harmonic emissions by regulating the creation of doublon-holon pairs. The complex temporal profile of HHG is elucidated in this work by the light-induced evolution of quasiparticle bands in correlated materials. In addition, the dephasing of the HHG spectrum caused by the vibration-induced disorder or lattice temperature is affirmed in the correlated electron systems and this dephasing process is attributed to quasiparticle-lattice scattering during the doublons and holons propagating among the disordered lattice sites.The key optical and electronic functionalities in condensed materials are determined by the band filling of electrons and their Coulomb correlations. To directly capture how many-body correlations influence the correlated electron dynamics under the driving of laser pulses, the comprehensible quasiparticle picture is desired to distinguish the ultrafast creation and annihilation of doublon-holon pairs in attosecond timescale. Here, we adopt the one-dimensional non-half-filling Hubbard model to study the high-harmonic generation (HHG) in correlated electron systems. As the value of Hubbard $U$ increases, the cutoff energy and spectral features in HHG spectra have been revealed and their scaling laws are explained by the characteristic energy gaps obtained from the electronic bands under the quasiparticle picture. The adjustable degree of band filling in correlated systems paves a way to enhance high-harmonic emissions by regulating the creation of doublon-holon pairs. The complex temporal profile of HHG is elucidated in this work by the light-induced evolution of quasiparticle bands in correlated materials. In addition, the dephasing of the HHG spectrum caused by the vibration-induced disorder or lattice temperature is affirmed in the correlated electron systems and this dephasing process is attributed to quasiparticle-lattice scattering during the doublons and holons propagating among the disordered lattice sites.

Physical review. B./Physical review. BOct 16, 202311 citations

Quasiparticel Spectra of the Hubbard Model

James F. Annett, William H. Beere

APSMar 1, 19980 citations

U

increases, the cutoff energy and spectral features in HHG spectra have been revealed and their scaling laws are explained by the characteristic energy gaps obtained from the electronic bands under the quasiparticle picture. The adjustable degree of band filling in correlated systems paves a way to enhance high-harmonic emissions by regulating the creation of doublon-holon pairs. The complex temporal profile of HHG is elucidated in this work by the light-induced evolution of quasiparticle bands in correlated materials. In addition, the dephasing of the HHG spectrum caused by the vibration-induced disorder or lattice temperature is affirmed in the correlated electron systems and this dephasing process is attributed to quasiparticle-lattice scattering during the doublons and holons propagating among the disordered lattice sites.