Topological quantum critical points exhibit anomalous dynamical scaling in boundary dynamics and defect production due to edge modes, beyond conventional Kibble-Zurek scaling.
Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
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abstract
Topological phenomena in quantum critical systems have recently attracted growing attention, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, a general framework for identifying such nontrivial phenomena, particularly in higher-dimensional systems, remains insufficiently explored. In this work, we propose a universal fingerprint for detecting nontrivial topology in critical free-fermion systems protected by global on-site symmetries. Specifically, we analytically establish an exact relation between the bulk entanglement spectrum and the boundary energy spectrum at topological criticality in arbitrary dimensions, demonstrating that the degeneracy of edge modes can be extracted from the bulk entanglement spectrum. These findings, further supported by numerical simulations of lattice models, provide a universal fingerprint for identifying nontrivial topology in critical free-fermion systems.
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PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.
A quantum channel applied near the entanglement cut maps the reduced density matrix of trivial gSPT states to non-trivial ones, thereby predicting their boundary CFT entanglement spectra.
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Anomalous Dynamical Scaling at Topological Quantum Criticality
Topological quantum critical points exhibit anomalous dynamical scaling in boundary dynamics and defect production due to edge modes, beyond conventional Kibble-Zurek scaling.
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PT symmetry-enriched non-unitary criticality
PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.
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A Framework for Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension
A quantum channel applied near the entanglement cut maps the reduced density matrix of trivial gSPT states to non-trivial ones, thereby predicting their boundary CFT entanglement spectra.