  From the perspective of thermal fluctuations, we investigate the pseudogap
phenomena in underdoped high-temperature curpate superconductors. We present a
local update Monte Carlo procedure based on the Green's function method to
sample the fluctuating pairing field. The Chebyshev polynomial method is
applied to calculate the single-particle spectral function directly and
efficiently. The evolution of Fermi arcs as a function of temperature is
studied by examining the spectral function at Fermi energy as well as the loss
of spectral weight. Our results signify the importance of the vortex-like phase
fluctuation on the formation of Fermi arcs.
