Quantum criticality of a one-dimensional Bose-Fermi mixture

TL;DR

This paper analytically investigates the quantum critical behavior of a one-dimensional Bose-Fermi mixture, revealing universal scaling laws and phase diagrams through Bethe ansatz methods, with implications for understanding many-body quantum critical phenomena.

Contribution

It provides an analytical study of the quantum phase diagram and criticality of 1D Bose-Fermi mixtures using thermodynamic Bethe ansatz, including effects of harmonic trapping.

Findings

Thermodynamical properties show universal scaling at quantum critical points.

Quantum criticality studied in both bulk and trapped systems.

Phase diagram and critical features elucidated for many-body quantum systems.

Abstract

The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study quantum phase diagram, equation of state and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behaviour at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in an harmonic trap is also studied within the local density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insights into understanding universal features of many-body critical phenomena.