Spectral functions of the one-dimensional Hubbard model in the U→+∞ limit:How to use the factorized wave function

Abstract

We give the details of the calculation of the spectral functions of the one-dimensional Hubbard model using the spin-charge factorized wave function for several versions of the U\ensuremath{\rightarrow}+\ensuremath{\infty} limit. The spectral functions are expressed as a convolution of charge and spin dynamical correlation functions. A procedure to evaluate these correlation functions very accurately for large systems is developed, and analytical results are presented for the low-energy region. These results are fully consistent with the conformal field theory. We also propose a direct method of extracting the exponents from the matrix elements in more general cases.