The possibility to form excitons in photoilluminated correlated materials is central from fundamental and application oriented perspectives. In this paper we show how the interplay of electron-electron interactions and a magnetic superstructure leads to the formation of a peculiar spinful dark exciton, which can be detected in ARPES-type experiments and optical measurements. We study this by using matrix product states (MPS) to compute the time evolution of single-particle spectral functions and of the optical conductivity following an electron-hole excitation in a class of one-dimensional correlated band-insulators, simulated by Hubbard models with on-site interactions and alternating local magnetic fields. An excitation in only one specific spin direction leads to an additional band in the gap region of the spectral function only in the spin direction unaffected by the excitation and to an additional peak in the optical conductivity. As both is formed only after the excitation, this is interpreted as a dark exciton, which shows only in one spin direction. Recombination of the excitation happens on much longer time scales than the ones amenable to MPS. We discuss implications for experimental studies in correlated insulator systems.
The possibility to form excitons in photoilluminated correlated materials is central from fundamental and application oriented perspectives. In this paper we show how the interplay of electron-electron interactions and a magnetic superstructure leads to the formation of a peculiar spinful dark exciton, which can be detected in ARPES-type experiments and optical measurements. We study this by using matrix product states (MPS) to compute the time evolution of single-particle spectral functions and of the optical conductivity following an electron-hole excitation in a class of one-dimensional correlated band-insulators, simulated by Hubbard models with on-site interactions and alternating local magnetic fields. An excitation in only one specific spin direction leads to an additional band in the gap region of the spectral function only in the spin direction unaffected by the excitation and to an additional peak in the optical conductivity. As both is formed only after the excitation, this is interpreted as a dark exciton, which shows only in one spin direction. Recombination of the excitation happens on much longer time scales than the ones amenable to MPS. We discuss implications for experimental studies in correlated insulator systems.
In this thesis we numerically study non-equilibrium phenomena in one-dimensional quantum many-body systems. We discuss extensions of the concepts of spectral functions and of the optical conductivity to time-dependent non-equilibrium setups and compute these quantities by means of matrix product state (MPS)-based methods. In a first application we study the effect of a spin-selective particle-hole-like excitation on a Hubbard model with an additional magnetic superstructure. Following the excitation, this model exhibits a stable charge density, as well as a stable spin density pattern mirroring the superstructure. For interacting systems we find an additional in-gap signal in the spectral function in the spin direction opposite to the one we applied the excitation in, which also persists over time. Our results are confirmed by a computation of the corresponding optical conductivity. We interpret our results as a trace of an exciton, which we support by an analysis in the atomic limit, and therefore refer to our findings as a peculiar spinful exciton. In contrast to many other setups, no long-range Coulomb term is needed for this exciton to form. Second, we apply the same calculus to compute non-equilibrium spectral functions of a Floquet-driven system of interacting spinless fermions in the charge density wave (CDW) Mott insulator phase, where we model the driving through a Peierls substitution ansatz. We find good agreement of our results with computations from an effective model obtained from Floquet theory, as well as Floquet side bands. These, however, do not show at all times as expected. Furthermore, another in-gap signal occurs, that is somewhat reminiscent of free particles, which goes hand in hand with a melting of the CDW pattern.
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.
We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.
The real part of optical conductivity $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ by modeling the electron-phonon coupling present in La2CuO4 and Nd2CuO4, we obtain $\text{Re}\ensuremath{\sigma}(\ensuremath{\omega})$ comparable with experiments.
We study the formation of itinerant electronic states on carrier doping in a strongly correlated insulator by calculating one-particle-excitation spectral functions. We apply (1) the quantum Monte Carlo method and (2) the exact diagonalization method in the framework of the dynamical mean field theory to a two-band Hubbard model. The parameters of the model are chosen so that the undoped system is a charge-transfer-type insulator. We find that the itinerant states originate from local singlet states formed by hybridized d - and p -holes. We also find asymmetry between hole-doped and electron-doped cases: (1) in the electron-doped case a peak is not observed at the chemical potential in contrast to the hole-doped case; and (2) the mass-enhancement factor in the electron-doped case is smaller than that in the hole-doped case. The results of the one-particle-excitation spectrum and the mass-enhancement factor are discussed in the light of experimental and theoretical results for high- T c cuprates.
The real part of optical conductivity, Reσ(ω), of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study Reσ(ω) of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of Reσ(ω) not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well-defined. The emergence of an excitonic peak in Reσ(ω) implies the formation of a spin polaron. Examining the dependence of Reσ(ω) on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in Reσ(ω) by modeling the electron-phonon coupling present in La2CuO4 and Nd2CuO4, we obtain Reσ(ω) comparable with experiments.