arXiv subjects

Taegon Lee

Publications and source records attributed to Taegon Lee.

3 recordsLinked to original sources

arXiv2026

Wavefunctions for Anyon Superconductors

Anyon superconductivity arises from the condensation of mobile anyons rather than from a conventional Cooper instability, yet a systematic wavefunction description remains lacking. We develop a hierarchy-wavefunction construction for superconducting states derived from parent topological orders and identify their off-diagonal long-range order, condensate charge, chiral central charge, and residual topological order through the plasma analogy and topological field theories. We construct Abelian and non-Abelian examples descending from the semion state, a $\nu=2/3$ hierarchy state, the $\nu=1/3$ Laughlin state, $\nu=1$ integer quantum Hall state, and Pfaffian state. Remarkably, for the semion case, the superconducting many-semion wavefunction is equivalent to a state of fermionized anyons filling two effective Landau levels, recovering Laughlin's original construction of semion superconductor. Finally, we show that hierarchy wavefunctions emerge naturally in the dilute, long-distance limit of the anyon-Hilbert-space formulation, which applies to ideal Chern bands and moir\'e bands of twisted bilayer MoTe$_2$. Our results establish a unified wavefunction-level framework linking anyon condensation, superconducting order, and topological field theory.

cond-mat.str-el↗

arXiv2026

$\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau Theory of Fractional Quantum Hall Hierarchies

We construct effective $\mathrm{U}(2)$ Chern-Simons-Ginzburg-Landau theories for Abelian and non-Abelian fractional quantum Hall hierarchies for those which had previously been described only through categorical data or trial wavefunctions. Our framework captures both Abelian hierarchy states built on half-filled Pfaffian-type parents and non-Abelian hierarchies emerging from Abelian states. It reproduces all filling fractions obtained from wavefunction and categorical constructions and, moreover, uniquely determines the corresponding topological orders. We also identify an intriguing particle-hole symmetry relating two hierarchy sequences, one built on a trivial insulator and the other on the $\nu=1$ integer quantum Hall state, which respectively generate the Read-Rezayi sequences and their particle-hole conjugates under the same hierarchy construction.

cond-mat.str-el↗

arXiv2026

A Unified Categorical Description of Quantum Hall Hierarchy and Anyon Superconductivity

We present a unified category-theoretic framework for quantum Hall hierarchy constructions and anyon superconductivity based on modular tensor categories over $\mathrm{Rep}(\mathrm{U}(1))$ and $\mathrm{sRep}(\mathrm{U}(1)^f)$. Our approach explicitly incorporates conserved $\mathrm{U}(1)$ charge and formulates doping via a generalized stack-and-condense procedure, in which an auxiliary topological order is stacked onto the parent phase, and the quasiparticles created by doping subsequently condense. Depending on whether this condensation preserves or breaks the $\mathrm{U}(1)$ symmetry, the system undergoes a transition to a quantum Hall hierarchy state or to an anyon superconductor. For anyon superconductors, the condensate charge is determined unambiguously by the charged local bosons contained in the condensable algebra. Our framework reproduces all known anyon superconductors obtained from field-theoretic analyses and further predicts novel phases, including a charge-$2e$ anyon superconductor derived from the Laughlin state and charge-$ke$ anyon superconductors arising from bosonic $\mathbb{Z}_k$ Read-Rezayi states. By placing hierarchy transitions and anyon superconductivity within a single mathematical formalism, our work provides a unified understanding of competing and proximate phases near experimentally realizable fractional quantum Hall states.

cond-mat.str-el↗