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arXiv:2410.13664 · Physical review. B./Physical review. B

Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders

E. Merhej, J. P. Hague, Robert Konik, A. J. A. James

Published Mar 17, 2026• 0 citations

Abstract

Using matrix product state techniques we study the nonequilibrium dynamical response of the half-filled Hubbard ladder when subject to an optical pump. Optical pumping offers a way of producing and manipulating new strongly correlated phenomena by suppressing existing magnetic correlations. The ladder allows the effects of pump directionality to be investigated, and compared to a single chain it has strong spin-charge coupling and a fully gapped excitation spectrum, promising different nonequilibrium physics. We compute time-dependent correlations, including the nonequilibrium dynamical structure factors for spin and charge. By deriving a combined spin-charge sum rule that applies both in and out-of-equilibrium, we show that spectral weight is pumped directly from the antiferromagnetic spin response into a low energy ω ∼ 0 charge response below the Mott gap. The transfer of weight is pump direction dependent: pumping directed along the legs disrupts magnetic correlations more than pumping in the rung-direction, even if the post-pump energy density is similar. The charge correlation length is dramatically enhanced by the pump, whilst the spin correlations are most strongly suppressed at nearest- and next-nearest-neighbor spacings. After the pump the system is in a nonthermal correlated metallic state, with gapless charge excitations and approximately equal spin and charge correlation lengths, emphasizing the importance of treating these degrees of freedom on an equal footing in nonequilibrium systems.

DOI: 10.1103/f9zt-ckbp

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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 present a computational technique to calculate time- and momentum-resolved nonequilibrium spectral density of correlated systems using a tunneling approach akin to scanning tunneling spectroscopy. The important difference is that our probe is extended, basically a copy of the sample, allowing one to extract the momentum information of the excitations. We illustrate the method by measuring the spectrum of a Mott-insulating extended Hubbard chain after a sudden quench with the aid of time-dependent density-matrix renormalization-group calculations. We demonstrate that the system realizes a nonthermal state that is an admixture of spin and charge density wave states, with corresponding signatures that are recognizable as in-gap subbands. In particular, we identify a band of excitons and one of stable antibound states at high energies that gains enhanced visibility after the pump. We do not appreciate noticeable relaxation within the time scales considered, which is attributed to the lack of decay channels due to spin-charge separation. These ideas can be readily applied to study transient dynamics and spectral signatures of correlation-driven nonequilibrium processes.

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We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing

U/t

converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of

U/t

of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.