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Hall-on-Toric State: Descendant Laughlin State in the Chiral Z_{p} Toric Code.

Robin Schäfer1,2,3, Claudio Chamon4,5, Chris R Laumann1,6

  • 1Boston University, Department of Physics, Boston, Massachusetts 02215, USA.

Physical Review Letters
|May 11, 2026
PubMed
Summary

The chiral Z_{p} toric code exhibits new topological phases called Hall-on-Toric states. These states feature fractionalized charges and higher ground-state degeneracy, confirmed by iDMRG simulations.

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Area of Science:

  • Condensed Matter Physics
  • Topological Quantum Matter
  • Quantum Information

Background:

  • The chiral Z_{p} toric code is a fundamental model for topological order.
  • Understanding emergent topological phases is crucial for quantum computing and materials science.

Purpose of the Study:

  • To investigate emergent topological phases in the chiral Z_{p} toric code under perturbation.
  • To characterize the properties of these novel Hall-on-Toric states.

Main Methods:

  • Utilizing infinite density matrix renormalization group (iDMRG) simulations.
  • Analyzing topological entanglement entropy, entanglement spectra, and generalized Hall conductance.

Main Results:

  • Discovery of emergent Hall-on-Toric phases, a type of fractional quantum Hall-like state.
  • These phases exhibit fractionalized Z_{p} charges and enhanced topological ground-state degeneracy.
  • Hall-on-Toric states are robust, persisting even without U(1) symmetry.

Conclusions:

  • The chiral Z_{p} toric code hosts richer topological structures than previously understood.
  • Findings support a deeper interpretation of defects as excitations in topological phases.
  • This work opens new avenues for exploring hierarchical topological states.