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Springer eBooks

Single Hole Dynamics in Correlated Insulators

Michael Brunner, C. Lavalle, Sylvain Capponi, M. Feldbacher, Fakher F. Assaad, Alejandro Muramatsu

Published Jan 1, 2002• 1 citation
Publisher
DOI
10.1007/978-3-642-56034-7_13

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Optical Spectra and Exciton in Correlated Insulators in Electron–Hole Systems

Yuh Tomio, Tetsuo Ogawa

We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.

Journal of the Physical Society of Japan•Oct 12, 2010•3 citations

Hole dynamics in a correlated system with impurity

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Physica B Condensed Matter•Jun 1, 1996•1 citation

Microscopic control and dynamics of a Fermi-Hubbard system

Ji, Geoffrey

Strongly correlated systems have rich and intriguing behaviors that have been at the focal point of modern condensed-matter physics. One promising research direction is the study of the Fermi-Hubbard model, which is thought to describe the essential physics of the cuprates and is naturally realized with ultracold atoms in optical lattices. The development of single-site control and readout on this platform has allowed for new methods in creating and studying states in the Fermi-Hubbard model. In this thesis, we discuss the engineering of low-entropy correlated states using a novel technique. By preparing a gapped band-insulator in the presence of an entropy reservoir, we create states with an entropy per particle of 0.016(3) k_B. We then demonstrate that the low-entropy band insulator can be used as a resource for creating strongly correlated states; by dynamically manipulating the on-site potentials we are able to convert the uncorrelated band insulator into a correlated Mott insulator. We also investigate if heating is responsible for the increase in entropy when creating the correlated phase and determine that it does not play a dominant role. In a separate experiment, we leverage the single-site manipulation capabilities in a different way by creating a single localized hole dopant in an antiferromagnetic state. We then allow the hole to delocalize by suddenly removing its pinning potential and study the resulting density and spin correlation evolution. As the hole delocalizes, we find that it displaces the surrounding spin correlations in a trajectory that is initially controlled by quantum interference. At later times, the hole delocalizes at a rate that scales with the spin exchange energy, revealing that the presence of magnetism fundamentally alters charge transport. These developments demonstrate continued progress in optical lattice quantum simulators and how they can play a role in unraveling the mysteries of the Fermi-Hubbard model.

•Jan 1, 2021•0 citations

Metal-Insulator Transitions in Strongly Correlated Systems

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Springer proceedings in physics•Jan 1, 1998•0 citations

Correlation strength, gaps, and particle-hole asymmetry in high- T c cuprates: A dynamical mean field study of the three-band copper-oxide model

Luca de’ Medici, Xin Wang, Massimo Capone +1 more

The three-band model relevant to high-temperature copper-oxide superconductors is solved using single-site dynamical mean field theory and a tight-binding parametrization of the copper and oxygen bands. For a band filling of one hole per unit cell the metal/charge-transfer-insulator phase diagram is determined. The electron spectral function, optical conductivity, and quasiparticle mass enhancement are computed as functions of electron and hole doping for parameters such that at one hole per cell the paramagnetic phase is insulating and for parameters such that at one hole per unit cell the paramagnetic phase is metallic. The optical conductivity is computed using the Peierls phase approximation for the optical matrix elements. The calculation includes the physics of ``Zhang-Rice singlets.'' The effects of antiferromagnetism on the magnitude of the gap and the relation between correlation strength and doping-induced changes in state density are determined. Three-band and one-band models are compared. The two models are found to yield quantitatively consistent results for all energies less than about 4 eV including energies in the vicinity of the charge-transfer gap. Parameters on the insulating side of the metal/charge-transfer insulator phase boundary lead to gaps which are too large and near-gap conductivities which are too small relative to data. The results place the cuprates clearly in the intermediate correlation regime, on the paramagnetic metal side of the metal/charge-transfer insulator phase boundary.

arXiv:0804.2250•Physical Review B•Aug 4, 2009•58 citations

Metal-insulator transition in highly correlated systems

C. A. Büsser, E. V. Anda, Laura Urba +2 more

Journal of Magnetism and Magnetic Materials•Jan 1, 1998•2 citations
We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.
Strongly correlated systems have rich and intriguing behaviors that have been at the focal point of modern condensed-matter physics. One promising research direction is the study of the Fermi-Hubbard model, which is thought to describe the essential physics of the cuprates and is naturally realized with ultracold atoms in optical lattices. The development of single-site control and readout on this platform has allowed for new methods in creating and studying states in the Fermi-Hubbard model. In this thesis, we discuss the engineering of low-entropy correlated states using a novel technique. By preparing a gapped band-insulator in the presence of an entropy reservoir, we create states with an entropy per particle of 0.016(3) k_B. We then demonstrate that the low-entropy band insulator can be used as a resource for creating strongly correlated states; by dynamically manipulating the on-site potentials we are able to convert the uncorrelated band insulator into a correlated Mott insulator. We also investigate if heating is responsible for the increase in entropy when creating the correlated phase and determine that it does not play a dominant role. In a separate experiment, we leverage the single-site manipulation capabilities in a different way by creating a single localized hole dopant in an antiferromagnetic state. We then allow the hole to delocalize by suddenly removing its pinning potential and study the resulting density and spin correlation evolution. As the hole delocalizes, we find that it displaces the surrounding spin correlations in a trajectory that is initially controlled by quantum interference. At later times, the hole delocalizes at a rate that scales with the spin exchange energy, revealing that the presence of magnetism fundamentally alters charge transport. These developments demonstrate continued progress in optical lattice quantum simulators and how they can play a role in unraveling the mysteries of the Fermi-Hubbard model.
The three-band model relevant to high-temperature copper-oxide superconductors is solved using single-site dynamical mean field theory and a tight-binding parametrization of the copper and oxygen bands. For a band filling of one hole per unit cell the metal/charge-transfer-insulator phase diagram is determined. The electron spectral function, optical conductivity, and quasiparticle mass enhancement are computed as functions of electron and hole doping for parameters such that at one hole per cell the paramagnetic phase is insulating and for parameters such that at one hole per unit cell the paramagnetic phase is metallic. The optical conductivity is computed using the Peierls phase approximation for the optical matrix elements. The calculation includes the physics of ``Zhang-Rice singlets.'' The effects of antiferromagnetism on the magnitude of the gap and the relation between correlation strength and doping-induced changes in state density are determined. Three-band and one-band models are compared. The two models are found to yield quantitatively consistent results for all energies less than about 4 eV including energies in the vicinity of the charge-transfer gap. Parameters on the insulating side of the metal/charge-transfer insulator phase boundary lead to gaps which are too large and near-gap conductivities which are too small relative to data. The results place the cuprates clearly in the intermediate correlation regime, on the paramagnetic metal side of the metal/charge-transfer insulator phase boundary.