In Chapter 9 we developed the picture of the asymptotics of the correlation functions of the Hubbard model for the phases with gapless excitations, i.e., for the phases with ground states belonging to regions II and IV of the ground state phase diagram discussed in Chapter 6.3 (see figures 6.4, 6.5). Our results relied on the predictions of conformal field theory which are expected to hold for a whole universality class of models related to the Hubbard model and which only need the finite size data calculated in Chapter 8 as input parameters. Correlation functions at half-filling (phase V) were considered in the previous chapter on the basis of a special continuum limit and the predictions of certain integrable quantum field theories.

Here we shall consider correlation functions in the phase whose ground state is the empty band (phase I in the ground state phase diagram, figures 6.4, 6.5). At zero temperature the boundary of this phase in the μ-B plane (see figure 6.5) is determined by equation (6.20): μ < μ0(B). For small finite temperature a small number of particles is populating the system. They form a dilute, thermodynamically ideal gas with pressure proportional to the temperature (see below). We shall say the system is in the gas phase [176] and shall give a more precise meaning to this statement later.