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arXiv:2010.13255 · Physical review. B./Physical review. B

High-harmonic generation in one-dimensional Mott insulators

Yuta Murakami, Shintaro Takayoshi, Akihisa Koga, Philipp Werner

Published Jan 8, 2021• 64 citations

Abstract

We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e., a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.

DOI: 10.1103/physrevb.103.035110

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We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e., a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.

To study excitonic effects on high-harmonic generation (HHG) in Mott insulators, we investigate pumped nonequilibrium dynamics in the one-dimensional extended Hubbard model. By employing time-dependent calculations based on the exact diagonalization and infinite time-evolving block decimation methods, we find the strong enhancement of the HHG intensity around the exciton energy. The subcycle analysis in the sub-Mott-gap regime shows that the intensity region of the time-resolved spectrum around the exciton energy splits into two levels and oscillates following the driving electric field. This excitonic dynamics is qualitatively different from the dynamics of free doublon and holon but favorably contributes to HHG in the Mott insulator.

High-harmonic generation (HHG) in strongly correlated Mott insulators is investigated using exact diagonalization and time-dependent density-matrix propagation of a laser-driven one-dimensional Hubbard chain. By projecting onto equilibrium Hubbard bands, we use the doublon population and its dynamics as a diagnostic to analyze intraband (spin-wave-like) and interband (doublon-holon creation) excitation channels. A filling-dependent crossover emerges: Bloch-like intraband response at dilute filling, mixed dynamics at intermediate filling, and interband-dominated HHG with plateau and cutoff near half filling. In the considered parameter range, increasing interaction strength

U

strongly suppresses interband contributions through the enlarged Mott gap and correlation-induced localization. Intra- and interband current decomposition reveals opposing flows below the Mott gap (Δ_{\mathrm{Mott}}) and selective dephasing suppression of interband coherence, enhancing net doublon accumulation. Time-frequency analysis uncovers the filling-dependent features of quantum trajectories, manifesting in distinct below-Δ_{\mathrm{Mott}} emission. This doublon-based analysis provides a transparent link between equilibrium spin-charge separation and nonequilibrium strong-field response, and clarifies how dephasing modifies interband coherence and doublon accumulation.

We study the high harmonic generation (HHG) in Mott insulators using Floquet dynamical mean-field theory (DMFT). We show that the main origin of the HHG in Mott insulators is the doublon-holon recombination, and that the character of the HHG spectrum differs depending on the field strength. In the weaker-field regime, the HHG spectrum shows a single plateau as in the HHG from gases, and its cut-off energy

ε_{\rm cut}

scales linearly with the field strength

E_0

as

ε_{\rm cut}=Δ_{\rm gap} + αE_0

, where

Δ_{\rm gap}

is the Mott gap. On the other hand, in the stronger-field regime, multiple plateaus emerge and the

m

-th cut-off scales as

ε_{\rm cut,m}=U + m E_0

. We show that this difference originates from the different dynamics of the doublons and holons in the weak- and strong-field regimes. We also comment on the similarities and differences between HHG from Mott insulators and from semiconductors. This proceedings paper complements our recent work, Phys. Rev. Lett. 121, 057405 (2018), with additional results and analyses.

Using Floquet dynamical mean-field theory, we study the high-harmonic generation in the time-periodic steady states of wide-gap Mott insulators under ac driving. In the strong-field regime, the harmonic intensity exhibits multiple plateaus, whose cutoff energies ε_{cut}=U+mE_{0} scale with the Coulomb interaction U and the maximum field strength E_{0}. In this regime, the created doublons and holons are localized because of the strong field and the mth plateau originates from the recombination of mth nearest-neighbor doublon-holon pairs. In the weak-field regime, there is only a single plateau in the intensity, which originates from the recombination of itinerant doublons and holons. Here, ε_{cut}=Δ_{gap}+αE_{0}, with Δ_{gap} the band gap and α>1. We demonstrate that the Mott insulator shows a stronger high-harmonic intensity than a semiconductor model with the same dispersion as the Mott insulator, even if the semiconductor bands are broadened by impurity scattering to mimic the incoherent scattering in the Mott insulator.

We unveil multifaceted effects of spin-charge couplings on the high-harmonic generation (HHG) in Mott insulators by analyzing the two-leg ladder Hubbard model, where spin dynamics activated by the interchain hopping t_{y} drastically modifies the HHG features. When the two chains are decoupled (t_{y}=0), HHG originates from the dynamics of coherent doublon-holon pairs because of spin-charge separation. With increasing t_{y}, the doublon-holon pairs lose their coherence due to their interchain hopping and resultant nonlocal spin strings. Furthermore, the HHG signal from spin polarons-charges dressed by spin clouds-leads to an additional plateau in the HHG spectrum. For large t_{y}, we identify unconventional HHG processes involving three elementary excitations-two polarons and one magnon. Our study is an essential step toward a microscopic understanding of nontrivial many-body effects on HHG in correlated materials beyond conventional semiconductors.

The high-harmonic spectrum of the Mott insulating Hubbard model has recently been shown to exhibit plateau structures with cutoff energies determined by

n\mathrm{th}

-nearest-neighbor doublon-holon recombination processes. The spectrum thus allows one to extract the on-site repulsion

U

. Here, we consider generalizations of the single-band Hubbard model and discuss the signatures of bosonic excitations in high-harmonic spectra. Specifically, we study an electron-plasmon model which captures the essential aspects of the dynamically screened Coulomb interaction in solids and a multiorbital Hubbard model with Hund coupling which allows one to analyze the effect of local spin excitations. For the electron-plasmon model, we show that the high-harmonic spectrum can reveal information about the screened and bare on-site interaction, the boson frequency, as well as the relation between boson coupling strength and boson frequency. In the multiorbital case, string states formed by local spin excitations result in an increase of the radiation intensity and cutoff energy associated with higher-order recombination processes.