Emergent ballistic transport of Bose-Fermi mixtures in one dimension

TL;DR

This paper investigates the ballistic transport phenomena in one-dimensional Bose-Fermi mixtures, revealing how conserved charges and quasiparticle excitations lead to segmented light-cone hydrodynamics and novel transport properties.

Contribution

It provides the first rigorous analytical study of transport in 1D Bose-Fermi mixtures using generalized hydrodynamics and Bethe ansatz, demonstrating multiple light-cone structures.

Findings

Existence of conserved charges for bosonic and fermionic degrees of freedom.

Analytical density and current distributions depend on x/t ratio.

Observation of segmented light-cone hydrodynamics with ballistic transport.

Abstract

The degenerate Bose-Fermi (BF) mixtures in one dimension present a novel realization of two decoupled Luttinger liquids with bosonic and fermionic degrees of freedom at low temperatures. However, the transport properties of such decoupled Luttinger liquids of charges have not yet been studied. Here we apply generalized hydrodynamics to study the transport properties of one-dimensional (1D) BF mixtures with delta-function interactions. The initial state is set up as the semi-infinite halves of two 1D BF mixtures with different temperatures, joined together at the time $t=0$ and the junction point $x=0$. Using the Bethe ansatz solution, we first rigorously prove the existence of conserved charges for both the bosonic and fermionic degrees of freedom, preserving the Euler-type continuity equations. We then analytically obtain the distributions of the densities and currents of the local conserved quantities which solely depend on the ratio $\xi=x/t$. The left and right moving quasiparticle excitations of the two halves form multiple segmented light-cone hydrodynamics that display ballistic transport of the conserved charge densities and currents in different degrees of freedom. Our analytical results provide a deep understanding of the quantum transport of multi-component Luttinger liquids in quantum systems with both bosonic and fermionic statistics.