Fluctuations in heat current and scaling dimension

TL;DR

This paper investigates the universal relationship between heat current fluctuations and the heat current in 1+1D chiral systems, revealing a connection to the scaling dimension that can probe exotic quantum states.

Contribution

It introduces a theoretical framework using scattering and conformal field theory to relate heat current fluctuations to the scaling dimension in chiral systems.

Findings

The ratio of heat current fluctuations to the heat current is proportional to the scaling dimension.

Results are consistent across scattering theory and conformal field theory approaches.

Findings can be used to probe fractional and non-Abelian quantum states.

Abstract

In this work, we theoretically study the heat flow between two $1+1$d chiral gapless systems connected by a point contact. With a small temperature gradient between the two, we find that the ratio between fluctuations of the heat current and the heat current itself is proportional to the scaling dimension -- a universal number that characterizes the distribution of the particles tunneling through the point contact. We adopt two different approaches, scattering theory and conformal field theory, to calculate this ratio and see that their results agree. Our findings are useful for probing not only fractional charge excitations in fractional quantum Hall states but also neutral ones in non-Abelian phases.