An algebraic second-quantization for 1D Abelian anyons with phase θ=π/N is constructed, together with an exact Jordan-Wigner duality that maps π/3 anyons onto spin-1 operators.
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Disorder induces a crossover from phase-averaging to mode-mixing regimes in domain wall transport of a second-order topological insulator, marked by a 0.5 e²/h plateau and two-step conductance fluctuations at 0.35 and 0.29 e²/h with corresponding Fano factors of 1/4 and 1/3.
Fermi seas with the same Euler characteristic χ_F possess distinct fine-grained topological structures captured by a new structural resolution factor, which topological superconductors inherit to produce anomalous gapless boundary states.
Degeneracies of energy levels in the Kitaev quantum double model for arbitrary discrete group G and genus are expressed via S-matrix elements, giving the exact partition function for finite systems.
Lattice models with engineered quantum geometry host Abelian and non-Abelian fractional Chern insulators, anomalous Hall crystals, and Halperin states, with the N=2 model realizable in twisted MoTe₂.
Long-range correlated disorder creates a non-self-averaging topological Anderson insulator phase with non-vanishing Lyapunov exponent variance and non-Gaussian distributions that violate the central limit theorem.
Derives discretely spaced complex spectra and biorthogonal eigenstates for non-Hermitian Landau levels under complex magnetic fields, confirmed via a Harper-Hofstadter lattice model.
Tuning the angle between sites in an OAM l=1 staggered lattice switches the winding number and number of topologically protected edge states in a Creutz-ladder mapping.
The second plateau at about 3/5 the first in 3D QHE arises from spin-density-wave order induced by nesting between spin-up and spin-down Landau bands after a Lifshitz transition.
Non-Abelian multigap topology with Euler class invariants in kagome NHC MOFs induces a controllable magnetononlinear Hall effect.
A variational generalized Landau-level mapping shows the first moiré valence band supports Jain-sequence Abelian states while the Hartree-Fock-renormalized second band hosts a non-Abelian Moore-Read state at filling 5/2 for twist angle 2.45°.
CF exciton trial states accurately capture collective mode dispersions in spinful FQH states on the sphere at all wavelengths, while density-wave states miss high-energy parton modes in singlet cases at fillings like 2/5.
A Monte Carlo method maps quantum Fisher information lower bounds for explicit many-body wavefunctions to classical expectation values, enabling efficient computation under decoherence for Jastrow-Gutzwiller states.
The spatially random localized phase at low filling factors in bilayer graphene is the disorder-induced Anderson solid phase.
Numerical tests confirm that modular Hamiltonian methods extract expected topological numbers from FQHE wavefunctions but converge reliably only on large lattices.
A review summarizing theoretical and experimental progress on disorder-induced topological phases including TAIs, quasiperiodic extensions, non-Hermitian systems, and many-body realizations.
citing papers explorer
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Second quantization of anyons and spin-anyon duality
An algebraic second-quantization for 1D Abelian anyons with phase θ=π/N is constructed, together with an exact Jordan-Wigner duality that maps π/3 anyons onto spin-1 operators.
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Disorder-induced crossover from phase-averaging to mode-mixing regimes in magnetic domain walls of a second-order topological insulator
Disorder induces a crossover from phase-averaging to mode-mixing regimes in domain wall transport of a second-order topological insulator, marked by a 0.5 e²/h plateau and two-step conductance fluctuations at 0.35 and 0.29 e²/h with corresponding Fano factors of 1/4 and 1/3.
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Fine-grained topological structures hidden in Fermi sea
Fermi seas with the same Euler characteristic χ_F possess distinct fine-grained topological structures captured by a new structural resolution factor, which topological superconductors inherit to produce anomalous gapless boundary states.
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Partition function of the Kitaev quantum double model
Degeneracies of energy levels in the Kitaev quantum double model for arbitrary discrete group G and genus are expressed via S-matrix elements, giving the exact partition function for finite systems.
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Quantum-Geometric Design of Lattice Generalized Landau Levels
Lattice models with engineered quantum geometry host Abelian and non-Abelian fractional Chern insulators, anomalous Hall crystals, and Halperin states, with the N=2 model realizable in twisted MoTe₂.
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Non-self-averaging topological Anderson insulator
Long-range correlated disorder creates a non-self-averaging topological Anderson insulator phase with non-vanishing Lyapunov exponent variance and non-Gaussian distributions that violate the central limit theorem.
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Non-Hermitian Landau Levels
Derives discretely spaced complex spectra and biorthogonal eigenstates for non-Hermitian Landau levels under complex magnetic fields, confirmed via a Harper-Hofstadter lattice model.
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Geometrical control of topology with orbital angular momentum modes
Tuning the angle between sites in an OAM l=1 staggered lattice switches the winding number and number of topologically protected edge states in a Creutz-ladder mapping.
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3D Quantum Hall Effect with Two Distinct Plateaus
The second plateau at about 3/5 the first in 3D QHE arises from spin-density-wave order induced by nesting between spin-up and spin-down Landau bands after a Lifshitz transition.
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Magnetononlinear Hall effect from multigap topology in metal-organic frameworks
Non-Abelian multigap topology with Euler class invariants in kagome NHC MOFs induces a controllable magnetononlinear Hall effect.
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Abelian and non-Abelian fractionalized states in twisted MoTe$_2$: A generalized Landau-level theory
A variational generalized Landau-level mapping shows the first moiré valence band supports Jain-sequence Abelian states while the Hartree-Fock-renormalized second band hosts a non-Abelian Moore-Read state at filling 5/2 for twist angle 2.45°.
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Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
CF exciton trial states accurately capture collective mode dispersions in spinful FQH states on the sphere at all wavelengths, while density-wave states miss high-energy parton modes in singlet cases at fillings like 2/5.
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Quantum Fisher Information under decoherence with explicit wavefunctions
A Monte Carlo method maps quantum Fisher information lower bounds for explicit many-body wavefunctions to classical expectation values, enabling efficient computation under decoherence for Jastrow-Gutzwiller states.
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Disorder-induced strong-field strong-localization in 2D systems
The spatially random localized phase at low filling factors in bilayer graphene is the disorder-induced Anderson solid phase.
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Testing the robustness of topological quantities evaluated from the modular Hamiltonian for a given wavefunction
Numerical tests confirm that modular Hamiltonian methods extract expected topological numbers from FQHE wavefunctions but converge reliably only on large lattices.
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Recent progress on disorder-induced topological phases
A review summarizing theoretical and experimental progress on disorder-induced topological phases including TAIs, quasiperiodic extensions, non-Hermitian systems, and many-body realizations.
- Computable fermionic non-Gaussianity from the covariance matrix