On the spacing distributions in the spin-1/2 XX chain

We provide a pedagogical calculation of the first two spacing distribution for a spin-1/2 XX chain in the presence of an external magnetic field. The results obtained from analytical expressions are compared with those from extensive quantum Monte Carlo simulations. The results obtained for the spacing distributions are used to describe the magnetic behavior of the system and contrasted with the standard analysis based on quantities such as the average energy, magnetization, and susceptibility. Finally, the equivalence between the analytical expressions for the spacing distributions provided by the second quantization formalism and those from the inter-particle distribution method is illustrated. As shown, the spacing distributions can be used as pedagogical examples of the use of the second quantization formalism in introductory courses of quantum statistical mechanics. Additionally, these distributions can be calculated easily from quantum Monte Carlo simulation and, therefore, can be used to illustrate this numerical method.

Keywords:
Emptiness distribution; spin chain; Wigner surmise; spacing distribution functions