### This is not the current version.

- Other versions of this Submission (with Reports) exist:
- version 2 (current version)

As Contributors: | Rodrigo Pereira |

Arxiv Link: | http://arxiv.org/abs/1706.02421v1 |

Date submitted: | 2017-06-12 |

Submitted by: | Pereira, Rodrigo |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Quantum Physics |

Using a perturbative renormalization group approach, we show that the extended ($J_1$-$J_2$-$J_d$) Heisenberg model on the kagome lattice with a staggered chiral interaction ($J_\chi$) can exhibit a gapless chiral quantum spin liquid phase. Within a coupled-chains construction, this phase can be understood as a chiral sliding Luttinger liquid with algebraic decay of spin correlations along the chain directions. We calculate the low-energy properties of this gapless chiral spin liquid using the effective field theory and show that they are compatible with the predictions from parton mean-field theories with symmetry-protected line Fermi surfaces. These results may be relevant to the state observed in the kapellasite material.

Has been resubmitted

1- The authors approach the problem from different perspectives (coupled chains and parton mean fields), and find not inconsistent results.

2- The authors provide a detailed account of their calculation.

3- The topic is timely.

4- The approach is in principle a very good one to address questions such as "is it in principle possible to find this or that phase", as is the goal of the paper.

1- There are technical concerns (see below) that have to be clarified.

2- The non-inconsistent results are not very specific (some out of many possible parton mean fields show the same behaviour as the coupled wires, it is left unclear if they are the appropriate ones).

I have two main concerns.

The first one is related to one of the central results of the paper, namely the strong coupling analysis of the sine-Gordon term in Eq. (50). The authors state that this term leads, in its strong coupling phase, to the formation of a gapless chiral spin liquid, and the opening of a partial gap. Crucial for this conclusion is the pinning of the argument of the sine-Gordon term, see Eq. (51). However, what is the meaning of "right" and "left" for right-movers and left-movers in different q-chains, given that they are not parallel? This is obviously crucial for the relative sign of the commutator between fields of different qs, which the authors impose in the decoupled chain limit (where this question does not arise), and hence for whether the argument of the cosine can be pinned at all (which can be the case if the argument commutes with itself at different positions). Since this is not the most simple sine-Gordon situation, the authors have to clarify their technical treatment.

The second concern is about the comparison to the parton mean field construction. It is well known that, being a complicated mean field approach, parton constructions are somewhat arbitrary. They should hence be guided by some physical intuition: why is one parton construction chosen rather than another? In the precise case, the authors just pick from a list of mean field constructions the ones that have a spin correlation function decaying as 1/r^2. But is there any other reason for why the chosen patron states are good ones? In particular, I note that the authors find both a Z2 gauge field construction, and a U(1) gauge field construction to give the 1/r^2 decay, and hence two very different states. The conclusion can thus merely the hat one can find parton construction that happen to have the same decay of correlations as the coupled chain construction. Given the arbitrariness of parton mean fields, this is somewhat unsatisfactory. Can the authors find a more convincing argument as to why the parton mean fields they pick are relevant to their analysis?

1- The authors have to clarify their technical treatment of the sine-Gordon term for the entire paper to be considered scientifically correct.

2- The authors should expand their discussion of the parton mean fields, and be more precise about how much the comparison to parton mean fields is really telling us.

- validity: poor
- significance: ok
- originality: high
- clarity: ok
- formatting: excellent
- grammar: excellent