Phase diagrams of trivial phases in class A non-interacting fermions exhibit topological textures from non-trivial state families, computed via higher Berry phases, with diabolical points hosting robust boundary modes.
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A silicon photonics waveguide network implements quantum graphs, experimentally confirming that strongly chaotic versions exhibit random matrix theory spectral statistics unlike less chaotic ones.
A non-Bloch framework is established for nonlinear eigenvalue problems to reproduce open-boundary spectra and reveal unique phenomena plus topological correspondence.
A Krylov staggering parameter derived from Lanczos coefficients analytically distinguishes topological phases in the short-range Kitaev model and tracks boundary versus bulk control of the gap in long-range cases.
Local twist operators and a purity-gap-based chiral marker provide practical real-space indicators of topology in finite-temperature mixed states of the SSH model.
2DEG-S hybrids in quantized magnetic field host topologically protected edge states carrying even-integer quantized spin current robust to disorder.
Majorana flat bands in topological superconductors cause the system to form pair density waves or phase crystals that lower free energy by gapping zero-energy states, with the uniform solution never surviving at zero temperature.
A one-dimensional array of periodically modulated defects in scattering states produces tunable emergent topological phases with nontrivial band winding and a stable Thouless charge pump.
In the non-Hermitian Kitaev chain, preserved particle-hole symmetry makes the open-chain topological transition coincide with the periodic one and forces zero-energy Majorana modes to appear as reciprocal localization pairs that cancel the non-Hermitian skin effect.
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
Nonsymmorphic 1D four-band models with Kramers degeneracy support Z2 and Z4 invariants computed via extended open-path winding numbers, realized in topolectric circuits whose impedance reproduces phase boundaries and zero-energy modes that remain pinned under minimal disorder.
Finite current flux fragilizes the two-mode topological phase in a Kitaev ladder, shown via bulk invariants and edge-edge quantum conditional mutual information.
A class-C N-channel quantum network model with random tunneling is mapped to a nonlinear sigma model in the large-N limit, with triplet modes typically massive except under specific conditions, and Zeeman field breaking additional symmetries.
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Textured phase diagrams of featureless insulators
Phase diagrams of trivial phases in class A non-interacting fermions exhibit topological textures from non-trivial state families, computed via higher Berry phases, with diabolical points hosting robust boundary modes.
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Quantum chaos with graphs: a silicon photonics plateform
A silicon photonics waveguide network implements quantum graphs, experimentally confirming that strongly chaotic versions exhibit random matrix theory spectral statistics unlike less chaotic ones.
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Non-Bloch band theory of nonlinear eigenvalue problems
A non-Bloch framework is established for nonlinear eigenvalue problems to reproduce open-boundary spectra and reveal unique phenomena plus topological correspondence.
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Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures
A Krylov staggering parameter derived from Lanczos coefficients analytically distinguishes topological phases in the short-range Kitaev model and tracks boundary versus bulk control of the gap in long-range cases.
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Characterizing topology at nonzero temperature: Topological invariants and indicators in the extended SSH model
Local twist operators and a purity-gap-based chiral marker provide practical real-space indicators of topology in finite-temperature mixed states of the SSH model.
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Emergent spin quantum Hall edge states at the boundary of two-dimensional electron gas proximitized by an $s$-wave superconductor
2DEG-S hybrids in quantized magnetic field host topologically protected edge states carrying even-integer quantized spin current robust to disorder.
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Nonuniform superconducting states from Majorana flat bands
Majorana flat bands in topological superconductors cause the system to form pair density waves or phase crystals that lower free energy by gapping zero-energy states, with the uniform solution never surviving at zero temperature.
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Emergent topological phase from a one-dimensional network of defects
A one-dimensional array of periodically modulated defects in scattering states produces tunable emergent topological phases with nontrivial band winding and a stable Thouless charge pump.
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Symmetry and Topology in a Non-Hermitian Kitaev chain
In the non-Hermitian Kitaev chain, preserved particle-hole symmetry makes the open-chain topological transition coincide with the periodic one and forces zero-energy Majorana modes to appear as reciprocal localization pairs that cancel the non-Hermitian skin effect.
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Krylov Complexity Under Hamiltonian Deformations and Toda Flows
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic states and supersymmetric systems.
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One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
Nonsymmorphic 1D four-band models with Kramers degeneracy support Z2 and Z4 invariants computed via extended open-path winding numbers, realized in topolectric circuits whose impedance reproduces phase boundaries and zero-energy modes that remain pinned under minimal disorder.
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Current-driven reduction of topological protection in multichannel superconductors
Finite current flux fragilizes the two-mode topological phase in a Kitaev ladder, shown via bulk invariants and edge-edge quantum conditional mutual information.
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The class C quantum network model with random tunneling and its nonlinear sigma model representation
A class-C N-channel quantum network model with random tunneling is mapped to a nonlinear sigma model in the large-N limit, with triplet modes typically massive except under specific conditions, and Zeeman field breaking additional symmetries.