Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures

We investigate magnetic properties and statistical effects in one-dimensional (1D) strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetization, and susceptibility in the presence of an external magnetic field H are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value HcF ≈ 8 γ EF, where EF is the Fermi energy and γ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0 and the critical value H= HcM ≈ 16 γ EF. We find that a pure boson phase occurs in the absence of the external field, fully polarized fermions and bosons coexist for 0<H< HcM, and a fully polarized fermion phase occurs for H≥ HcM. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.