Anyon superfluid in trilayer quantum Hall systems

Taige Wang; Ya-Hui Zhang

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arXiv · 2508.00058

Anyon superfluid in trilayer quantum Hall systems

Taige Wang·Ya-Hui Zhang

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Abstract

Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at $\nu_{1}=\nu_{2}=\nu_{3}= \frac13$, tuned solely by the inter-layer spacing $d$, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate ``anyon-exciton condensate'' separating the familiar $\nu_{\mathrm{tot}}=1$ exciton condensate ($d \to 0$) from three decoupled Laughlin liquids ($d \to \infty$). In this phase, neutral bi-excitons condense while a $\nu=\frac23$ Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistivity $R_{xy}=\frac{5}{2} h/e^{2}$, both within reach of existing high-mobility trilayer devices.

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Taige Wang, Ya-Hui Zhang. 2025-07-31. Anyon superfluid in trilayer quantum Hall systems. https://arxiv.org/abs/2508.00058

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