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Spectral function of the $U \rightarrow \infty$ one dimensional Hubbard model at finite temperature and the crossover to the spin incoherent regime

The physics of the strongly interacting Hubbard chain (with $t/U \ll 1$) at finite temperatures undergoes a crossover to a spin incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective "spin temperature". We use the time-dependent density matrix renormalization group method (tDMRG) to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by $k_F$ of the minimum of the dispersion.