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arXiv:2305.09909 · Physical review. B./Physical review. B

Pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling

K. Sugimoto, Satoshi Ejima

Published Nov 14, 2023• 7 citations
arXivHTMLPDF

Abstract

By utilizing time-dependent tensor-network algorithms in the infinite matrix-product-state representation, we theoretically investigate the pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling. Our focus lies on nonequilibrium optical conductivity and single-particle excitation spectra. In the spin-density-wave (SDW) phase, we identify an in-gap state in the nonequilibrium optical conductivity due to the formation of excitons (or doublon-holon pairs), generated by the pulse through nonlocal interactions. In the strong-coupling regime, we discern additional multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase, we detect not only an in-gap state but also a finite Drude weight, which results from the dissolution of charge order by photoexcitation. Analyzing time-dependent single-particle excitation spectra directly in the thermodynamic limit confirms the origin of these new states in the SDW and CDW phases as the excitation of newly emerged dispersions. We illustrate that the pump-probe spectroscopy simulations in the thermodynamic limit furnish unambiguous spectral structures that allow for direct comparison with experimental results, and the integration of nonequilibrium optical conductivity and time- and angle-resolved photoemission spectroscopy provides comprehensive insights into nonequilibrium states.

DOI
10.1103/physrevb.108.195128

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By utilizing time-dependent tensor-network algorithms in the infinite matrix-product-state representation, we theoretically investigate the pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling. Our focus lies on nonequilibrium optical conductivity and single-particle excitation spectra. In the spin-density-wave (SDW) phase, we identify an in-gap state in the nonequilibrium optical conductivity due to the formation of excitons (or doublon-holon pairs), generated by the pulse through nonlocal interactions. In the strong-coupling regime, we discern additional multiple in-gap and out-of-gap states. In the charge-density-wave (CDW) phase, we detect not only an in-gap state but also a finite Drude weight, which results from the dissolution of charge order by photoexcitation. Analyzing time-dependent single-particle excitation spectra directly in the thermodynamic limit confirms the origin of these new states in the SDW and CDW phases as the excitation of newly emerged dispersions. We illustrate that the pump-probe spectroscopy simulations in the thermodynamic limit furnish unambiguous spectral structures that allow for direct comparison with experimental results, and the integration of nonequilibrium optical conductivity and time- and angle-resolved photoemission spectroscopy provides comprehensive insights into nonequilibrium states.
We investigate the time evolution of optical conductivity in the half-filled one-dimensional extended Hubbard model driven by a transient laser pulse, by using the time-dependent Lanczos method. Photoinduced in-gap excitations exhibit a qualitatively different structure in the spin-density wave (SDW) in comparison to the charge-density-wave (CDW) phase. In the SDW, the origin of a low-energy in-gap excitation is attributed to the even-odd parity of the photoexcited states, while in the CDW an in-gap state is due to confined photogenerated carriers. The signature of the in-gap excitations can be identified as a characteristic oscillation in the time evolution of physical quantities.
We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.
Abstract Motivated by the recent progress in time-resolved nonequilibrium spectroscopy in condensed matter, we study an optically excited one-dimensional ionic Hubbard model by exact diagonalization. The model is relevant to organic crystals, transition metal oxides, or ultracold atoms in optical lattices. We implement numerical pump-probe measurements to calculate time-dependent conductivity and single-particle spectral functions. In general, short optical excitation induces a metallic behavior imprinted as a Drude peak in conductivity or an in-gap density of states. In a Mott insulator, we find that the induced Drude peak oscillates at the pump frequency and its second harmonic. The former comes from the oscillation of currents, and the latter from the interference of single- and three-photon excited states. In a band insulator, the Drude peak oscillates only at the pump frequency, and quantities such as the double occupancy do not oscillate. The absence of the second harmonic oscillation is due to the degeneracy of multi-photon excited states. The in-gap density of states in both insulators correlates with the Drude weight and the energy absorption for weak pumping. Strong pumping leads to saturation of the in-gap density of states and to suppression of the Drude weight in the Mott regime. We have also checked that the above features are robust for insulators in the intermediate parameter range. Our study demonstrates the distinct natures of the multi-photon excited states in two different insulators.
The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by the Gaussian and the spin-gap transitions under charge-spin separation, or by a direct CDW-SDW transition. We determine these phase boundaries by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and the spin-gap transitions take place separately from weak- to intermediate-coupling region. This means that the third phase exists between the CDW and the SDW states. Our results are also consistent with those of the strong-coupling perturbative expansion and of the direct evaluation of order parameters.
Abstract Utilizing the time-dependent Lanczos method, we investigate the photoexcitation dynamics of the one-dimensional (1D) extended Peierls–Hubbard model at quarter filling. In equilibrium, it is well established that introducing the nearest-neighbour interaction V into the 1D Peierls–Hubbard model can lead to the formation of Mott–Hubbard excitons, which exhibit a characteristic frequency in the optical conductivity that is lower than the Mott gap. Ultrafast photoexcitation of this model gives rise to a transient metallic state for V < 2, characterized by several features, including a zero-frequency Drude peak in the post-pump optical conductivity, an increase in the density of charge carriers, and enhanced electron hopping between dimers. In contrast, when V ≥ 2, this metallic state is no longer observed, as photoinduced carriers bind to form excitons, thereby inhibiting metallic behavior. These results highlight a parallel between the optical excitation of the 1D extended Peierls–Hubbard model at quarter filling and that of the 1D extended Hubbard model at half filling, suggesting a universal mechanism governing their photoinduced responses.
We investigate the short-time evolution of the half filled one-dimensional extended Hubbard model in the strong-coupling regime, driven by a transient laser pump. Combining twisted boundary conditions with the time-dependent Lanczos technique, we obtain snapshots of the single-particle spectral function with high momentum resolution. The analysis of the oscillations of the spectral function shows that its characteristic frequencies are consistent with the magnitudes of the optical gap. Furthermore, we examine the time-evolving spectral structure in the charge-density-wave phase in detail and find that one of the bands in the single-particle spectrum originates from the photoinduced bond-order background.