Abstract
Motivated by the recent work on QED3-Chern-Simons quantum critical points of fractional Chern insulators [Phys. Rev. X 8, 031015 (2018)], we study its non-Abelian generalizations, namely, QCD3-Chern-Simons quantum phase transitions of fractional Chern insulators. These phase transitions are described by Dirac fermions interacting with non-Abelian Chern-Simons gauge fields [U(N), SU(N), USp(N), etc.]. Utilizing the level-rank duality of Chern-Simons gauge theory and non-Abelian parton constructions, we discuss two types of QCD3 quantum phase transitions. The first type happens between two Abelian states in different Jain sequences, as opposed to the QED3 transitions between Abelian states in the same Jain sequence. A good example is the transition between σxy=1/3 state and σxy=−1 state, which has Nf=2 Dirac fermions interacting with a U(2) Chern-Simons gauge field. The second type is naturally involving non-Abelian states. For the sake of experimental feasibility, we focus on transitions of Pfaffian-like states, including the Moore-Read Pfaffian, anti-Pfaffian, particle-hole Pfaffian, etc. These quantum phase transitions could be realized in experimental systems such as fractional Chern insulators in graphene heterostructures.Received 7 June 2020Revised 7 August 2020Accepted 10 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033348Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChern insulatorsChern-Simons gauge theoryConformal field theoryFractional quantum Hall effectGauge theoriesQuantum criticalityQuantum phase transitionsPhysical SystemsGrapheneCondensed Matter, Materials & Applied PhysicsParticles & Fields
Highlights
Understanding phases and phase transitions is the key to condensed matter research
The recent experimentally advances on integer and fractional Chern insulators (ICIs and FCIs) in graphene heterostructures [11,12,13] brought disorder-free quantum Hall (QH) phase transitions within reach [14]
Bμ is integrated out, which yields a Chern-Simons term 1/4kπ αdα. This family of QED3-Chern-Simons quantum critical points was previously studied using the language of composite fermions; here we will reformulate it using the parton construction that is useful for the rest of this paper
Summary
Understanding phases and phase transitions is the key to condensed matter research. A cornerstone of the modern condensed matter research is the discovery and understanding of integer and fractional quantum Hall phases (IQHs and FQHs) [1,2,3], which inspires many interesting concepts, i.e., topological order, fractionalization, emergent gauge fields, in the last few decades [4,5]. Given its interesting properties and wide applications, there has been a large theoretical effort to study the properties of this family of critical theory [32,33,34,35,36,37,38], but its precise properties at small Nf and K remain an open issue due to its strongly interacting nature This makes its experimental exploration exciting, in particular the entire family of the QED3-Chern-Simons theory (with any combination of Nf and K) is accessible experimentally at the phase transitions of QH/CI phases. IV we provide parton constructions for these Pfaffian-like states, which are important building blocks for the following analysis on their phase transitions Some of these constructions are known, but they are scattered in different papers [46,48,51,53,62]. The Appendix contains various technical details regarding nonAbelian Chern-Simons descriptions of several Pfaffian-like states
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