Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders

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 $ω\sim 0$ 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 neighbour 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, emphasising the importance of treating these degrees of freedom on an equal footing in nonequilibrium systems.

💡 Research Summary

In this work the authors employ state‑of‑the‑art matrix‑product‑state (MPS) techniques to investigate the nonequilibrium dynamics of a half‑filled Hubbard ladder subjected to an ultrafast optical pump. The ladder consists of two coupled one‑dimensional Hubbard chains with leg hopping t∥ and rung hopping t⊥; in equilibrium both spin and charge excitations are gapped for any finite on‑site repulsion U, and the ground state displays strong antiferromagnetic (AF) correlations. The study focuses on the regime t∥=t⊥=1 and U=8 (in units of the hopping), which places the system deep in the Mott insulating phase.

The pump is introduced via a Peierls substitution that adds a time‑dependent vector potential A(t)=A0 exp