Dynamics of two-body operators in exactly solvable spin chains

Abstract

Quantum spin-1/2 chains exhibit exotic phenomena such as absence of magnetic order at zero temperature and spectrum with fractional excitations. The interpretation of experiments that probe the excitation spectrum, such as resonant inelastic x-ray scattering (RIXS), requires the calculation of dynamical correlation functions at finite energies, a challenge for conventional analytical methods. In this project, we propose a theoretical study of the two-spin dynamical structure factor for the XY model, which is equivalent to a lattice model of free fermions. The approach will consist of utilizing the Jordan-Wigner transformation to map the two-spin operator onto an operator that creates two particle-hole pairs in the fermionic representation. The line shape of the dynamical structure factor for the XY model will then be contrasted with equivalent results for the Heisenberg model.