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

Authors

Joachim Stolze
Angela Nöppert
Gerhard Müller, University of Rhode IslandFollow

Document Type

Article

Date of Original Version

8-1-1995

Abstract

Dynamic spin correlation functions <S_i^x(t)S_x^j> for the one-dimensional S = ½ XX model H = -JΣ_i{S_i^xS^x_i+l + S^y_iS^y_i+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 < T < ∞, 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 < T < ∞ (~ 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 <S^x_i(t)S^x_j>. 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.

Citation/Publisher Attribution

Joachim Stolze, Angela Nöppert, and Gerhard Müller. Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains. Phys. Rev. B 52 (1995), 4319-4326.

Available at: http://dx.doi.org/10.1103/PhysRevB.52.4319

Publisher Statement

Copyright 1995 The American Physical Society.