GAUSSIAN, EXPONENTIAL, AND POWER-LAW DECAY OF TIME-DEPENDENT CORRELATION-FUNCTIONS IN QUANTUM SPIN CHAINS

Dynamic spin correlation functions [S-i(x)(t)S-j(x)] for the one-dimensional S = 1/2 XX model H = -J Sigma(i){(SiSi+1x)-S-x + (SiSi+1v)-S-v} are calculated exactly for finite open chains with up to N = 10 000 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 = infinity, exponential at 0 < T < infinity, and power-law (similar to 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 (similar to t(-1)) and at 0 < T < infinity (similar to t(-3/2)), but is site dependent at T = infinity. 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 [S-i(x)(t)S-j(x)]. 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 not equal j.