Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function C mn ( t ) = 〈 ψ ( t ) ∣ c m † c n ∣ ψ ( t ) 〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn ( t ) = C mn ( t ) − C mn (∞) decays with time following the power law behavior t − μ , where the exponent μ depends on whether the quench is to the commensurate phase ( μ = 1) or incommensurate phase ( μ = 1 2 ). This decay of δ C mn ( t ) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.