Electrons are fundamental building blocks of nature and are indivisible in isolation. However, when electrons (or other quantum particles with an internal ``spin" degree of freedom) are confined in one spatial dimension, they loose their identity as individual particles, and ``break'' into separate excitations carrying spin, and charge, with each degree of freedom being characterized by a different energy scale. While the basic theoretical understanding of spin-charge separation in one-dimension, known as ``Luttinger liquid theory'', has existed for some time, recently a previously unidentified regime of strongly interacting one-dimensional systems at finite temperature came to light: The ``spin-incoherent Luttinger liquid". This occurs when the temperature is larger than the characteristic spin energy scale. The key to establishing both Luttinger liquid behavior and spin-incoherent Luttinger liquid behavior in experiment is detailed knowledge of the spectral properties.
I will present a numerical study of the finite-temperature spectral properties of a one-dimensional fermionic gas in the spin-incoherent regime using the time-dependent density matrix renormalization group method. This approach enables us to quantitatively handle the experimentally relevant and theoretically challenging "crossover" regime between the Luttinger liquid and spin-incoherent Luttinger liquid limits. I will discuss the possibility of observing spin-incoherent behavior in spin ladders, in the context of a recent neutron scattering experiment. Finally, I will show that spin-incoherent behavior can be realized in the ground-state of model Hamiltonians, such as Hubbard ladders, and the Kondo lattice.