Time-dependent correlations of tensor operators in quantum spin chains

Abstract

Dynamical correlation functions provide direct information about the propagation and decay of excitations in quantum many-body systems. Recent experiments in cold atomic gases and ion traps have fostered a particular interest in the time dependence of correlations, but theoretical results are still rather limited since, unlike equilibrium properties, the problem of dynamics is not well described by low-energy effective theories. In this masters project we propose a theoretical study of time-dependent correlation functions for the two-spin tensor operator in a spin-1/2 chain described by the XY model, which is exactly solvable. The approach will consist of using the Jordan-Wigner transformation to map the spin correlations onto correlations of fermionic operators calculated in a noninteracting ground state. We intend to investigate systematically all the components of the two-spin tensor, both in the cases in which the operators are local in the fermionic basis and in the cases of nonlocal operators that involve strings. (AU)