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

TL;DR

This paper analyzes magnetic properties and phase transitions in 1D strongly repulsive Fermi-Fermi and Bose-Fermi mixtures using exact thermodynamic solutions, revealing universal behaviors and phase diagrams with polarized and mixed phases.

Contribution

It provides the first detailed analysis of magnetic phase transitions and universality classes in strongly repulsive 1D Fermi and Bose-Fermi mixtures using the thermodynamic Bethe ansatz.

Findings

Polarized fermions exhibit antiferromagnetic behavior at zero temperature.

Universal linear field-dependent magnetization persists for weak and strong interactions.

Phase diagram includes fully polarized, mixed, and pure boson phases depending on external magnetic field.

Abstract

We investigate magnetic properties and statistical effects in 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 $H^F_c\approx \frac{8}{\gamma}E_F$, where $E_F$ is the Fermi energy and $\gamma$ 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 $H=H^M_c\approx \frac{16}{\gamma}E_F$. We find that a pure boson phase occurs in the absence of the external field, fully-polarized fermions and bosons coexist for $0<H<H^M_c$, and a fully-polarized fermion phase occurs for $H\ge H_c^M$. 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.