Perfect elliptic dichroism is proposed as a direct diagnostic for the metric of anisotropic quantum Hall droplets, extending to ideal Chern bands via holomorphicity and to lattice models via renormalized emergent metrics.
Modular transformation and bosonic/fermionic topological orders in Abelian fractional quantum Hall states
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abstract
The non-Abelian geometric phases of the robust degenerate ground states were proposed as physically measurable defining properties of topological order in 1990. In this paper we discuss in detail such a quantitative characterization of topological order, using generic Abelian fractional quantum Hall states as examples. We find a way to determine even the pure U(1) phase of the non-Abelian geometric phases. We show that the non-Abelian geometric phases not only contain information about the quasi-particle statistics, they also contain information about the chiral central charge Delta c mod 24 of the edge states, as well as the Hall viscosity. Thus, the non-Abelian geometric phases (both the Abelian part and the non-Abelian part) provide a quite complete way to characterize 2D topological order.
fields
cond-mat.mes-hall 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Circular dichroism signals from chiral metric-modulating drives directly measure Hall viscosity while frequency resolution separates it from other modes.
citing papers explorer
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Perfect elliptic dichroism: Probing the metric of anisotropic quantum Hall droplets
Perfect elliptic dichroism is proposed as a direct diagnostic for the metric of anisotropic quantum Hall droplets, extending to ideal Chern bands via holomorphicity and to lattice models via renormalized emergent metrics.
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Hall viscosity from metric-sensitive dichroic probes
Circular dichroism signals from chiral metric-modulating drives directly measure Hall viscosity while frequency resolution separates it from other modes.