Quantum Criticality of one-dimensional multicomponent Fermi Gas with Strongly Attractive Interaction

TL;DR

This paper analyzes the quantum critical behavior of a one-dimensional multicomponent Fermi gas with strong attraction and $SU(3)$ symmetry, revealing phase transitions, critical fields, and universal scaling laws using the thermodynamic Bethe ansatz.

Contribution

It provides analytical solutions for phase diagrams, equations of state, and scaling functions for strongly interacting $SU(3)$ Fermi gases, extending methods to multi-component systems.

Findings

Identified quantum phase transitions driven by chemical potential and magnetic fields.

Derived analytical expressions for equations of state and critical fields.

Established universal scaling exponents $z=2$ and $ u=1/2$ for the system.

Abstract

Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $\mu$, effective magnetic field $H_1$, $H_2$ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent $z=2$ and correlation length exponent $\nu=1/2$ read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with $SU(N)$ symmetry.