arXiv subjects

Jie-Yu Zhang

Publications and source records attributed to Jie-Yu Zhang.

5 recordsLinked to original sources

arXiv2026

Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices

Motivated by recent theoretical and experimental advances, hyperbolic lattices have emerged as a paradigmatic setting in which geometry becomes an active organizing principle of quantum systems. Their negative curvature, exponential volume growth, and non-Abelian translation symmetry make them fundamentally distinct from Euclidean lattices and give rise to rich geometry-dependent physics, but also hinder the direct application of well-established analytical and computational approaches originally developed for physical systems defined on Euclidean lattices. To establish a unified framework for geometry-dependent physics on Euclidean and hyperbolic lattices, we develop \textit{higher-order non-uniform cellular automata} (NUCA) as a local-to-global construction for translationally invariant regular lattices. This construction derives geometry-dependent update rules through a lattice-deforming procedure that embeds hyperbolic lattices into a Euclidean square lattice, thereby encoding hyperbolic geometry while preserving physical locality. It thus provides a systematic route toward quantum and classical physics on hyperbolic lattices. We demonstrate the framework in three applications ranging from quantum many-body physics to non-equilibrium statistical physics. First, on the hyperbolic $\{5,4\}$ lattice, a linear NUCA generates exactly solvable subsystem symmetry-protected topological (SSPT) models and spontaneous subsystem symmetry-breaking models. Second, as a quantum generalization, we construct non-uniform Clifford quantum cellular automata (CQCA) for the hyperbolic cluster state. Third, we formulate a probabilistic NUCA for directed percolation (DP) on the hyperbolic lattice.

quant-ph↗

arXiv2026

Fracton Topological Holography

Topological holography (TH), or SymTFT, realizes symmetries and dualities of a quantum system as boundary data of a topological bulk in one higher dimension. We formulate fracton topological holography (FTH), extending this mechanism from liquid topological orders to fracton stabilizer codes. The construction is organized as a general four-stage framework: prepare the bulk model and compute its excitations, determine boundary data and admissible gapped top boundaries, identify the low-energy preserving operator algebra together with its symmetry, relation, and twist data, and then switch among top boundaries to compare the induced boundary descriptions. As a type-I example, we develop FTH for the X-cube model with smooth and rough top boundaries; for a minimal effective Hamiltonian, both yield transverse-field plaquette Ising models, with exchanged subsystem symmetry and twist data, and the boundary switch is implemented by a linear-depth local unitary sequential quantum circuit (SQC). As a type-II example, we formulate FTH for Haah's cubic code in the Laurent-polynomial stabilizer formalism and analyze the natural $(Z)$ and $(X)$ top boundaries, which induce two two-dimensional qubit systems related locally by exchanging generalized plaquette Ising and transverse-field terms and nonlocally by a symmetry--relation duality. These results show that FTH is a genuine extension of TH to both type-I and type-II fracton orders. FTH therefore provides a concrete framework for organizing and understanding duality, with the prospect of offering a systematic route to new dualities.

quant-ph↗

arXiv2026

Fusion Rules of Mobility

In topological phases of matter, fusion rules dictate how anyonic topological charges combine. However, the transformation of quasiparticle mobility under fusion remains largely unexplored. In this letter, we reveal that restricted mobility classes obey their own complex multi-channel fusion algebras. We introduce a family of exactly solvable models with $\mathbb{Z}_2$ topological order enriched by subsystem symmetries to explicitly demonstrate these structures. Within this framework, mobility constraints arise from enforcing symmetries supported on specific subsets. When excitations fuse, these rigid geometric constraints interfere spatially. At the macroscopic level, this deterministic geometric interference manifests as a multi-channel fusion ring. We present three explicit mobility fusion phenomena realized in distinct models: (i) Fibonacci fusion rules; (ii) tensor products of Fibonacci rules; and (iii) lineon period transmutation.

quant-ph↗

arXiv2026

Spurious Strange Correlators in Symmetry-Protected Topological Phases

Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases, leading to false positives in SPT diagnosis. Focusing on 1D gapped bosonic/spin systems described by matrix product states (MPS), we trace the origin of these spurious signals in trivial SPT phases to the magnitude-degeneracy of the transfer matrix. We systematically classify three distinct mechanisms responsible for such degeneracy, each substantiated by concrete examples: (1) the presence of high-dimensional irreducible representations (abbreviated as \emph{irrep}) in the eigenspace corresponding to the entanglment spectrum (entanglement space); (2) a phase mismatch in symmetry representations between the target and reference states; and (3) long-range order arising from symmetry breaking. Our findings clarify the importance of the choice of proper reference states, providing a guideline to avoid pitfalls and correctly identify SPT order using strange correlators.

cond-mat.str-el↗

arXiv2024

Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators

In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications such as secret sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., line-like subsystems in the 2D cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is \textit{mixed-subsystem SPT} that has either fractal and line-like subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is \textit{chaotic-subsystem SPT} in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in square lattice can be locally simulated by an HOCA generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call \textit{multi-point strange correlators}. We propose a universal procedure to design the spatial configuration of the multi-point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi-point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long range behavior in SRE states.

cond-mat.str-el↗