TEMPERATURE AND MAGNETIC FIELD-DEPENDENT CORRELATORS OF THE EXACTLY INTEGRABLE (1+1)-DIMENSIONAL GAS OF IMPENETRABLE FERMIONS

We show that the finite-temperature equal-time field correlators of the exactly integrable (1 + 1)-dimensional gas of impenetrable fermions in a magnetic field can be expressed as the first Fredholm minor of a completely integrable linear operator. This result enables us to derive differential equations for quantum correlators and to obtain analytical fomulae for long-distance asymptotics. In particular, a formula for correlation length as a function of temperature and magnetic field is presented. Our analysis reveals the presence of two length scales, which separate short-distance, intermediate and extreme asymptotic domains. The importance of the cross-over region is emphasized.