Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias

1. Systematic consideration of:
- various observables;
- in both limiting regimes;
- of a general class of models.
2. Detailed theoretical expressions. Useful for future reference.

1. No clear punchline. It is not clear which of the observables show the most promise.

The paper is of very high quality. It systematically addresses the question of transport observables induced by a temperature bias in a quantum Hall tunnelling contact. The authors address multiple observables: the charge noise, the heat current, the heat current noise, and even the mixed charge-heat noise. The authors analyse the limiting cases of small and large temperature bias and compare the asymptotic predictions with the exact solutions.

Further, the authors systematically introduce an effective single-particle picture, where the tunnelling properties of fractional quasiparticles are represented in terms of a Fermi distribution and power-law density of states.

Despite the high quality of the work, I do not feel it meets the SciPost acceptance criteria.
The authors state that their work meets two:
(i) Present a breakthrough on a previously-identified and long-standing research stumbling block;
(ii) Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work.

Concerning (i), I fail to see a long-standing stumbling block in the paper's consideration.

Concerning (ii). The paper does bring a systematic consideration of the scaling dimension into the temperature bias studies - which is an important aspect previously absent for the works in the area. However, the potential for follow-up work is rather narrow: performing experiments (potentially, on various observables considered in the work).
The paper may barely surpass criterion (ii), yet I do not see it opening a large space for thought.

However, I feel significantly more comfortable recommending the work to be published in SciPost Physics Core. It easily meets both acceptance criteria: addressing an important problem with a high degree of originality and significantly advance the knowledge in the field.
This will be an important reference work in the future for the people interested to perform one or another experiment and compare it to the theoretical predictions.

1. In the discussion of $|\mathcal{C}^{(4)}| \ll |\mathcal{C}^{(2)}|$ after Eq. (28), this relation is not evident from the expressions. It would be appropriate to refer the reader to Fig. 2.

2. When citing [77-79], it would be appropriate to cite also https://link.aps.org/doi/10.1103/PhysRevB.61.10929. This is the earliest work on the topic that I know.

3. In Eq. (67), the formula needs to be amended to account for the possibility of negative energies.

4. The expression in Eq. (77) looks like a conventional Landauer-Buttiker formula: all the Fermi functions and DOS correspond to the energy $E$, offset by the appropriate chemical potentials. At the same time, Eqs. (68-69) include integrands evaluated at $E$ and $-E$, which ruins the analogy with the Landauer-Buttiker formalism. I ask the authors to check the validity of these formulas; and if the mismatch persists, to comment about it in the text.

5. Ref. 102 is the same as Ref. 31. Please remove the duplicate.

Accept in alternative Journal (see Report)

1- treats an important and current subject of research in the physics of nano electronic devices
2- develops an approach to quantum charge and heat transport in fractional quantum Hall quantum point contacts using the standard approach of chiral Luttinger liquids
3- provides a comprehensive overview of noise characteristics of heat and charge transport
4- develops a picture based on an effective density of states and noninteracting tunneling to explain the physics

1- contains a huge amount of results and it is not clear what is the main focus
2- many results are presented as lengthy formulas and they are not interpreted
3- results are mainly of theoretical interest since quantities like the mixed noise are not measurable currently
4- only results in the perturbative regime of weak backscattering or weak tunneling are presented

The authors study the charge and heat transport in a quantum point contact formed between two edge channels in the fractional quantum Hall regime. They focus on noise correlations in the transport, which should provide additional insight into the average currents. To this end, they present a comprehensive overview of the auto- and cross-correlations of charge and energy currents in a wide range of scaling parameters. The main goal is to show how the different quantities reflect the scaling dimensions and how they could be extracted experimentally.

In my opinion, the authors present a solid work that deserves to be published more or less in its present form. Regarding the acceptance criteria highlighted by the author, I find it less clear that they are all fulfilled: the manuscript does not really open a new path or research direction, but rather further develops a well-defined and established theoretical approach to study the various noise quantities. It is certainly a contribution to the field of fractional quantum Hall physics, but will most likely not lead to follow-up work outside this field. I'm also not convinced that it represents an important breakthrough of a research stumbling block. The way to relate the rather complicated results of the fully interacting theory to the effective non-interacting picture might have an impact on future research, but is somewhat hidden in the vast amount of results.

Given the strict criteria for acceptance in SciPost Physics, I would recommend that the authors make a substantial revision and highlight the main results in a compact form at the beginning. It is important that this summary be comprehensible to readers who are not specialists in chiral Luttinger liquids. Otherwise, the manuscript in its current form is acceptable for SciPost Physics Core, where it could be published without further review.

Ask for major revision