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Network construction of nonAbelian chiral spin liquids
by Hernan Bueno Xavier, Claudio Chamon, and Rodrigo G. Pereira
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Hernan Bueno Xavier · Rodrigo Pereira 
Submission information  

Preprint Link:  scipost_202211_00022v1 (pdf) 
Date accepted:  20230215 
Date submitted:  20221111 17:56 
Submitted by:  Bueno Xavier, Hernan 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We use a network of chiral junctions to construct a family of topological chiral spin liquids in two spatial dimensions. The chiral spin liquid phase harbors SU(2)$_k$ anyons, which stem from the underlying SU(2)$_k$ WZW models that describe the constituent spin chains of the network. The network exhibits quantized spin and thermal Hall conductances. We illustrate our construction by inspecting the topological properties of the SU(2)$_2$ model. We find that this model has emergent Ising anyons, with spinons acting as vortex excitations that bind Majorana zero modes. We also show that the ground state of this network is threefold degenerate on the torus, asserting its nonAbelian character. Our results shed new light on the stability of nonAbelian topological phases in artificial quantum materials.
Published as SciPost Phys. 14, 105 (2023)
Reports on this Submission
Anonymous Report 2 on 2023111 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202211_00022v1, delivered 20230111, doi: 10.21468/SciPost.Report.6512
Strengths
1. The paper presents a view of a nonabelian 2d topological phase constructed from 1d critical models, which are extremely well studied and understood. This makes the former accessible to people familiar with the latter.
2. The paper is written quite clearly and even pedagogically.
Weaknesses
1. The universal content of the described topological phase is wellknown. What this paper does is reproduce it, rather than obtain new conclusions.
2. As a construction, it has the defect that the chiral boundary condition is put in by hand. This is only a weak defect that does not affect the goals of the paper, and indeed makes readability easier. However it means that the model does not a priori appear especially realistic.
Report
I do recommend acceptance. The paper satisfies criterion 4 to "provide a novel and synergistic link between research areas", in this case 2d topological phases and 1d critical models. I also think that there is potential for followup work (criteria 3) for example to 2d critical theories.
Anonymous Report 1 on 20221220 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202211_00022v1, delivered 20221220, doi: 10.21468/SciPost.Report.6350
Strengths
1 A new theoretical approach to the description of nonAbelian
topological phases in two spatial dimensions starting with 1D spin chains.
It is an alternative to coupledwire constructions and in this respect
it could be very useful to find new physical realisations of exotic phases
of matter.
2 The paper is very well written, accessible for most readers in the field.
Weaknesses
1 The main weakness is that the authors started the approach
by postulating the existence of a chiral fixed point for the junction
for general values of k. For k>2 it requires many fine tunings to kill
unwanted relevant and marginal perturbations.
2 The analysis is restricted to k=2 and exploits the freefield
representation of SU(2)_2 CFT in terms a bosonic field and the Ising CFT.
It will be interesting to see wether the explicit construction of string
operators that implement the transport of quasiparticles around the torus could also be done in the k>2 case.
Report
In this paper, the authors have introduced a network construction of non
Abelian SU(2)_2 chiral spin liquid in two dimensions which exhibits Ising
anyons. Such an exotic phase has already been described in the past by
means of different coupled wires constructions. However, the latter
approach requires several fine tunings and specific interactions which are
difficult to realize in quantum materials. One interest of this paper is to
describe this phase with a network of chiral Y junctions on a honeycomb
lattice. The main assumption is that each Y junction is fine tuned to a chiral fixed point which is described by an SU(2)_k conformal field theory (CFT).
For k=2, the case of interest here, it requires the fine tuning of a single
relevant operator and a marginal one. The topological phase of the
nonAbelian chiral spin liquid phase are explicitly shown by exploiting
a free field representation of the SU(2)_2 CFT. In particular, they found
the correct edge states, described by a chiral SU(2)_2 CFT, the existence of a bulk gap, which is guaranteed by
the construction using a collection of a finite critical spin chains, the
description of the lowlying excitations, and the correct topological
degeneracy on the torus for Ising anyons.
The paper is very interesting and very well written. It provides a new
controllable analytical approach to the description of exotic topological
phases in two dimensions which could be useful to find
experimental realization of these phases in the context of artificial
materials. I strongly recommend the publication of this paper in SciPost
journal.
Requested changes
1 A very minor remark is the citation of the paper of Capponi et al., Phys.
Rev. B 88, 075132 (2013), which found an SU(2)_k quantum criticality in
ladder systems with ringexchange interactions for all k > 1.
For completeness, this paper could be cited together with
the series of papers [3539] on critical spin chains.