Theory of Disordered ν=5/2 Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram

Biao Lian Princeton Center for Theoretical Science, Princeton University Juven Wang Institute for Advanced Study, Princeton

Theoretical Physics mathscidoc:1802.39001

Fractional quantum Hall (FQH) system at Landau level filling fraction $\nu=5/2$ has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance $\sigma_{xy}=5e^2/2h$. Thermal Hall conductances of the Pf and APf states are quantized at $\kappa_{xy}=7/2$ and $\kappa_{xy}=3/2$ respectively in a proper unit. However, a recent experiment shows the thermal Hall conductance of $\nu=5/2$ FQH state is $\kappa_{xy}=5/2$. It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a $\kappa_{xy}=5/2$ phase. In this work, we do perturbative and non-perturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold $\Lambda_1$, which is lowered to an emergent U(1)$\times$U(1) symmetry at energy scales between $\Lambda_1$ and a higher value $\Lambda_2$, and is finally lowered to the composite fermion parity symmetry $\mathbb{Z}_2^F$ above $\Lambda_2$. Based on the emergent symmetries, we propose a specific phase diagram of the disordered $\nu=5/2$ FQH system, and show that a $\kappa_{xy}=5/2$ phase arises at disorder energy scales $\Lambda>\Lambda_1$. Furthermore, we show the gapped double-semion sector of $N_D$ closed domain walls contributes non-local topological degeneracy $2^{N_D-1}$, causing a low temperature peak in the heat capacity. We also implement a non-perturbative method to bootstrap generic topological 1+1D domain walls (2-surface defects) applicable to any 2+1D non-Abelian topological order.
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el); Topological Phases of Matter; Gauge theories; TQFT; Quantum Field Theories; Chiral bosons; Majorana modes; non-Abelian statistics
[ Download ] [ 2018-02-08 11:54:17 uploaded by juvenwang ] [ 118 downloads ] [ 0 comments ]
  • https://arxiv.org/abs/1801.10149, with 43 pages
@inproceedings{biaotheory,
  title={Theory of Disordered ν=5/2 Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram},
  author={Biao Lian, and Juven Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208115417567515916},
}
Biao Lian, and Juven Wang. Theory of Disordered ν=5/2 Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180208115417567515916.
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