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-dimen sional 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 s pins. Over a certain time range the results are free of finite-size ef fects and thus represent correlation functions of an infinite chain (b ulk regime) or a semi-infinite chain (boundary regime). In the bulk re gime, the long-time asymptotic decay as inferred by extrapolation is G aussian at T = infinity, exponential at 0 < T < infinity, and power-la w (similar to t(-1/2)) at T = 0, in agreement with exact results, In t he 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 lo w-temperature regime (T/J << 1), crossovers between different decay la ws can be observed in [S-i(x)(t)S-j(x)]. Additional crossovers are fou nd between bulk-type and boundary-type decay for i = j near the bounda ry, and between spacelike and timelike behavior for i not equal j.