The issue of ergodicity is often underestimated. The presence of zero-frequency excitations in bosonic Green's functions determine the appearance of zero-frequency momentum-dependent quantities in correlation functions. The implicit dependence of matrix elements make such quantities also relevant in the computation of susceptibilities. Consequently, the correct determination of these quantities is of great relevance and the well-established practice of fixing them by assuming the ergodicity of the dynamics is quite questionable as it is not justifiable a priori by no means. In this manuscript, we have investigated the ergodicity of the dynamics of the z component of the spin in the one-dimensional Heisenberg model with anisotropic nearest-neighbor and isotropic next-nearest-neighbor interactions. We have obtained the zero-temperature phase diagram in the thermodynamic limit by extrapolating Exact and Lanczos diagonalization results computed on chains with sizes L=6-26. Two distinct nonergodic regions have been found: one for J′ Jz 0.3 and J Jz <1 and another for J′ Jz 0.25 and J Jz =1. On the contrary, finite-size scaling of T≠0 results, obtained by means of Exact diagonalization on chains with sizes L=4-18, indicates an ergodic behavior of dynamics in the whole range of parameters. © 2006 The American Physical Society.
Nonergodic dynamics of the extended anisotropic Heisenberg chain
AVELLA, Adolfo;
2006-01-01
Abstract
The issue of ergodicity is often underestimated. The presence of zero-frequency excitations in bosonic Green's functions determine the appearance of zero-frequency momentum-dependent quantities in correlation functions. The implicit dependence of matrix elements make such quantities also relevant in the computation of susceptibilities. Consequently, the correct determination of these quantities is of great relevance and the well-established practice of fixing them by assuming the ergodicity of the dynamics is quite questionable as it is not justifiable a priori by no means. In this manuscript, we have investigated the ergodicity of the dynamics of the z component of the spin in the one-dimensional Heisenberg model with anisotropic nearest-neighbor and isotropic next-nearest-neighbor interactions. We have obtained the zero-temperature phase diagram in the thermodynamic limit by extrapolating Exact and Lanczos diagonalization results computed on chains with sizes L=6-26. Two distinct nonergodic regions have been found: one for J′ Jz 0.3 and J Jz <1 and another for J′ Jz 0.25 and J Jz =1. On the contrary, finite-size scaling of T≠0 results, obtained by means of Exact diagonalization on chains with sizes L=4-18, indicates an ergodic behavior of dynamics in the whole range of parameters. © 2006 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
