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The European Physical Journal Special Topics

Entanglement analysis of photoinduced $$\eta$$-pairing states

Satoshi Ejima, Florian Lange, Holger Fehske

Published Sep 4, 2023• 5 citations
Publisher

Abstract

Abstract Simulating the von Neumann and second-order Rényi entropies of driven Mott insulators, we examine the entanglement dynamics of the $$\eta$$ η -pairing state in the one-dimensional half-filled Hubbard model after pulse irradiation. Corresponding data are obtained by means of the infinite time-evolving block decimation technique directly in the thermodynamic limit. For optimal pump-pulse parameters the temporal course of the entanglement entropies shows the characteristic entanglement growth due to the increase of $$\eta$$ η -pairing correlations.

DOI
10.1140/epjs/s11734-023-00975-6

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Entanglement analysis of photoinduced η\etaη-pairing states
Abstract Simulating the von Neumann and second-order Rényi entropies of driven Mott insulators, we examine the entanglement dynamics of the η\etaη η -pairing state in the one-dimensional half-filled Hubbard model after pulse irradiation. Corresponding data are obtained by means of the infinite time-evolving block decimation technique directly in the thermodynamic limit. For optimal pump-pulse parameters the temporal course of the entanglement entropies shows the characteristic entanglement growth due to the increase of η\etaη η -pairing correlations.
Utilizing time-evolution techniques in (infinite) matrix-product-state representation, we study the non-equilibrium dynamics of driven Mott insulators and demonstrate photoinduced \eta η pairing directly in the thermodynamic limit. Analyzing the time evolution of the corresponding pairing correlations, we determine the optimal laser pump parameters for which long-range \eta η -pairing becomes dominant after pulse irradiation. The time-dependent photoemission spectra for this optimal pump parameter set show clear signatures of the photoinduced insulator-to-metal phase transition related to the formation of \eta η pairs.
We use time-evolution techniques for (infinite) matrix product states to calculate, directly in the thermodynamic limit, the time-dependent photoemission spectra and dynamic structure factors of the half-filled Hubbard chain after pulse irradiation.These quantities exhibit clear signatures of the photoinduced phase transition from insulator to metal that occurs because of the formation of so-called η pairs.In addition, the spin dynamic structure factor loses spectral weight in the whole momentum space, reflecting the suppression of antiferromagnetic correlations due to the buildup of η-pairing states.The numerical method demonstrated in this work can be readily applied to other one-dimensional models driven out of equilibrium by optical pumping.
Employing the density-matrix renormalization group technique in the matrix-product-state representation, we investigate the photoexcited superconducting correlations induced by the η-pairing mechanism in the half-filled Hubbard chain.We estimate the characteristic pair correlation function and verify the accuracy of our numerical results by comparison with exact-diagonalization data for small systems.The optimal parameter set of the pump that most enhances the η-pair correlations, is calculated in the strong-coupling regime.For such a pump, we explore the possibility of quasi-long-range order.
This thesis explores non-equilibrium phenomena in strongly correlated quantum systems, focusing on the half-filled one-dimensional Hubbard model at zero temperature in the thermodynamic limit. Using tensor network methods, particularly infinite matrix product states (iMPS), we simulate the real-time dynamics induced by optical pump pulses. A laser pulse is modeled by a time-dependent vector potential applied via the Peierls substitution, with dynamics computed using the infinite time-evolving block decimation (iTEBD) algorithm. We investigate the emergence of a superconducting-like eta-pairing state with off-diagonal long-range order (ODLRO) and confirm that eta-pairing correlations are significantly enhanced for certain pulse parameters. Additionally, signatures of dynamical quantum phase transitions (DQPTs) are observed in the Loschmidt echo rate function. Finite-entanglement scaling is employed to extract the central charge and analyze criticality of the ground state.
Based on the nonperturbative many-body time-dependent approach, photoinduced Hubbard band mixing by ultrashort laser pulse is found in a one-dimensional half-filled Hubbard model through the optical conductivity. The nonlinear development of Drude-like (metallic) weight in the resonant optical pumping (${\ensuremath{\omega}}_{\mathrm{pu}}\ensuremath{\approx}{E}_{g}$; ${\ensuremath{\omega}}_{\mathrm{pu}}$ is the pumping laser energy and Eg{E}_{g}Eg​ is the gap energy) indicates reconstruction and mixing of the upper and lower Hubbard bands, in contrast to the case of linear development in off-resonant pumping $({\ensuremath{\omega}}_{\mathrm{pu}}⪢{E}_{g})$ where the rigid band picture is valid. The photoemission response after the ultrashort pulse confirms our finding.