Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains

Dynamic spin correlation functions \u3cSix(t)Sxj\u3e for the one-dimensional S = ½ XX model H = -JΣi{SixSxi+l + SyiSyi+1} are calculated exactly for finite open chains with up to N = 10000 spins. Over a certain time range the results are free of finite-size effects and thus represent correlation functions of an infinite chain (bulk regime) or a semi-infinite chain (boundary regime). In the bulk regime, the long-time asymptotic decay as inferred by extrapolation is Gaussian at T = ∞, exponential at 0 \u3c T \u3c ∞, and power-law (~ t-1/2) at T = 0, in agreement with exact results. In the boundary regime, a power-law decay is obtained at all temperatures; the characteristic exponent is universal at T = 0 (~ r-1) and at 0 \u3c T \u3c ∞ (~ r -3/2), but is site dependent at T= ∞. In the high-temperature regime (T/J ≫ 1) and in the low-temperature regime (T/J ≪1), crossovers between different decay laws can be observed in \u3cSxi(t)Sxj\u3e. Additional crossovers are found between bulk-type and boundary-type decay for i = j near the boundary, and between spacelike and timelike behavior for i ≠ j