Characterizing universal topological phases beyond spatial embedding
Abstract
Although Hamiltonians govern wave-matter interactions, conventional characterizations of topological phases of matter require more than the Hamiltonian alone, relying on global invariants defined on closed reciprocal-space manifolds or local commutation relations with position operators. This spatial dependence precludes a unique characterization of topological phases on an abstract platform, whose Hamiltonian can be defined independently of its spatial embedding. Here we establish a framework for characterizing universal topological phases, grounded in the invariance of topological features under arbitrary Hamiltonian-preserving deformations. We construct a Hamiltonian-based spatial embedding that groups a system's constituents according to their connectivity. This embedding, which reproduces the results of conventional topological diagnostics in established systems, enables a coherent extension of topological phases to complex networks using the Hamiltonian alone, further highlighting exceptional robustness in small-world networks. Our results reshape the conceptual foundations of topological physics by decoupling topological characterization from prescribed physical platforms.
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BibTeX
@misc{yu2026characterizing,
title = {{Characterizing universal topological phases beyond spatial embedding}},
author = {Sunkyu Yu and Xianji Piao and Namkyoo Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29022},
eprint = {2610.29022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29022},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Characterizing universal topological phases beyond spatial embedding
AU - Sunkyu Yu
AU - Xianji Piao
AU - Namkyoo Park
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29022
UR - https://arxiv.org/abs/2610.29022
AB - Although Hamiltonians govern wave-matter interactions, conventional characterizations of topological phases of matter require more than the Hamiltonian alone, relying on global invariants defined on closed reciprocal-space manifolds or local commutation relations with position operators. This spatial dependence precludes a unique characterization of topological phases on an abstract platform, whose Hamiltonian can be defined independently of its spatial embedding. Here we establish a framework for characterizing universal topological phases, grounded in the invariance of topological features under arbitrary Hamiltonian-preserving deformations. We construct a Hamiltonian-based spatial embedding that groups a system's constituents according to their connectivity. This embedding, which reproduces the results of conventional topological diagnostics in established systems, enables a coherent extension of topological phases to complex networks using the Hamiltonian alone, further highlighting exceptional robustness in small-world networks. Our results reshape the conceptual foundations of topological physics by decoupling topological characterization from prescribed physical platforms.
ER -