Finite temperature dynamics of the Mott insulating Hubbard chain

We study the dynamical response of the half-filled one-dimensional(1d) Hubbard model for a range of interaction strengths $U$ and temperatures $T$ by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group (tDMRG) computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures $T\sim J=4t^2\mathrm{/}U$ for sufficiently large $U>4t$. At smaller values of $U$ and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.