arXiv subjects

Kailin Song

Publications and source records attributed to Kailin Song.

2 recordsLinked to original sources

arXiv2026

Scaling laws of entanglement entropy in fractal dimensions

Entanglement entropy scaling links geometry to quantum correlations and diagnoses quantum criticality. Fractal lattices extend this link to noninteger dimensions, where boundary and bulk dimensions are independent. It remains open which dimension governs entropy scaling and how strongly gap closing can enhance it. Nonlocal occupied-state projectors and the lack of translation symmetry obstruct standard methods. We overcome these obstacles and classify free-fermion entropy scaling with bounds set by the hopping across the subsystem boundary: an upper bound from its rank and the spectral gap, and a lower bound from how much it lowers the ground-state energy. With only negative-energy states filled and this energy lowering proportional to the boundary, the entanglement entropy obeys the boundary law $S_X=Θ\left(L_X^{d_{\mathrm b}}\right)$ under a uniform gap and satisfies $L_X^{d_{\mathrm b}}\lesssim S_X\lesssim L_X^{d_{\mathrm b}}\ln L_X$ when the gap closes no faster than algebraically. Here $L_X$ is the subsystem linear size and $d_{\mathrm b}$ the boundary dimension. Half occupation of the chiral zero modes gives a mixed-state entropy $S_X^{\mathrm{mix}}$ with $\max\left\{S_X,z_X\ln2\right\}\leqslant S_X^{\mathrm{mix}}\leqslant S_X+z_X\ln2$, where $z_X$ is the local zero-mode weight; an extensive $z_X$ thus makes $S_X^{\mathrm{mix}}$ follow the bulk dimension.

quant-ph↗

arXiv2025

Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry

Bulk-boundary correspondence is the foundational principle of topological physics, first established in the quantum Hall effect, where a $D$-dimensional topologically nontrivial bulk gives rise to $(D-1)$-dimensional boundary states. The advent of higher-order topology has generalized this principle to a hierarchical chain, enabling topological states to appear at $(D-2)$ or even lower-dimensional boundaries. To date, all known realizations of topological systems must require a topologically nontrivial bulk to initiate the chain of action for bulk-boundary correspondence. Here, in an acoustic crystal platform, we experimentally demonstrate an exception to this paradigm--embedded topology in a trivial bulk--where the bulk-boundary correspondence originates from a trivial bulk. Rather than relying on global symmetries, we employ projective crystal symmetry, which induces nontrivial topology not at the outset in the $D$-dimensional bulk, but midway through the correspondence hierarchy in lower-dimensional boundaries. We further realize a three-dimensional system exhibiting embedded topology that supports zero-dimensional topological states, achieving the longest possible chain of action for such an unconventional bulk-boundary correspondence in physical space. Our work experimentally establishes a new form of bulk-boundary correspondence initiated from a trivial bulk, opening additional degrees of freedom for the design of robust topological devices.

cond-mat.mes-hall↗