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There is a holographic correspondence between (1) nD quantum systems with symmetry C and (2) nD boundaries of the n+1D topological order Z(C), where Z(C) is mathematically the Drinfeld center of C. Such mysterious topological holography has numerous applications and consequences, especially in the recent emerging field of generalized symmetry. By a rigorous construction and proof in 1+1D, we show that the Drinfeld center Z(C) naturally arise as the category of fixed-point local tensors with symmetry C, thus revealing the origin of topological holography. This talk is based on arXiv:2412.07198.

The classical wave system has demonstrated itself as an excellent platform to realize and investigate novel phenomena and physics. The bedrock principle is to utilize the macroscopic quantities obtained from the homogenization or mean-field treatment. However, it usually deals with Hermitian problems and averages out fluctuations. Therefore, the presentation will cover two topics: non-Hermitian physics and Casimir effect. The first part focuses on the impact of non Hermitian ingredients on soliton formation and dynamics. By constructing a soliton phase diagram, two distinct soliton phases and their transitions are identified. A Wannier-function-based nonlinear Hamiltonian shows that soliton formation critically depends on how skin-mode localization and band nonreciprocity suppress or enhance wave dispersion. Both soliton phases have been demonstrated to be dynamically accessible from bulk and edge excitations. The second part discusses the influence of the metal’s surface electrons on Casimir forces. A three-dimensional frame transformation method has been established by embedding mesoscopic boundary conditions of electromagnetic fields. We find that mesoscopic Casimir forces are sensitive to the surface electron behavior, including spill-in and spill-out, as verified by the multiple scattering method and proximity force approximation. The mechanism has finally been revealed as Casimir softening distances rooted in quantum surface responses of electrons.

There is a holographic correspondence between (1) nD quantum systems with symmetry C and (2) nD boundaries of the n+1D topological order Z(C), where Z(C) is mathematically the Drinfeld center of C. Such mysterious topological holography has numerous applications and consequences, especially in the recent emerging field of generalized symmetry. By a rigorous construction and proof in 1+1D, we show that the Drinfeld center Z(C) naturally arise as the category of fixed-point local tensors with symmetry C, thus revealing the origin of topological holography. This talk is based on arXiv:2412.07198.