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

Abstract

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 ${H}_{c}^{F}\ensuremath{\approx}\frac{8}{\ensuremath{\gamma}}{E}_{F}$, where ${E}_{F}$ is the Fermi energy and $\ensuremath{\gamma}$ 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 $H={H}_{c}^{M}\ensuremath{\approx}\frac{16}{\ensuremath{\gamma}}{E}_{F}$. We find that a pure boson phase occurs in the absence of the external field, fully polarized fermions and bosons coexist for $0<H<{H}_{c}^{M}$, and a fully polarized fermion phase occurs for $H\ensuremath{\geqslant}{H}_{c}^{M}$. 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.