Peng Ye

We introduce the subdimensional entanglement entropy (SEE), defined on subdimensional entanglement subsystems (SESs) embedded in the bulk, as an entanglement-based probe of how geometry and topology jointly shape universal properties of quantum matter. By varying the dimension, geometry, and topology of the SES, we show that the subleading term of SEE exhibits sharply distinct responses in a series of stabilizer states representing fixed points of different phases, including cluster states, Z q topological orders, and fracton orders. Treating the reduced density matrix of an SES as a many-body mixed state supported on the SES manifold, we further establish a general correspondence between bulk stabilizers and mixed-state symmetries on SESs, separating them into strong and weak classes, and use it to identify strong-to-weak spontaneous symmetry breaking within SESs. Finally, for SESs with nontrivial SEE, we show that a set of weak symmetries acts as transparent patch operators of the corresponding strong symmetries. This motivates the notion of transparent composite symmetry, which remains robust under bipartition-factorized finite-depth quantum circuits that preserve SEE, and implies that a D -dimensional SES may holographically encode a ( D + 1 ) -dimensional topological order. These results establish SEE not only as a sharp probe of geometric-topological response, but also as a route from bulk pure-state entanglement to mixed-state symmetry and holography on subdimensional manifolds.

Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent limitations. In this work, we introduce the \textit{hyperfine structure of entanglement}, which decomposes entanglement contours known as the fine structure into particle-number cumulants. This measure exhibits a set of universal properties with its significance in quantum information science. We apply it across diverse contexts: in Fermi gases, establishing connections to mutual information and interacting conformal field theory; in AdS$_3$/CFT$_2$ holographic duality, unveiling finer subregion-subregion duality; and in Chern insulators, distinguishing between different quantum phases, especially topological gapped state and trivial gapped state. Our findings suggest experimental accessibility, offering fresh insights into quantum entanglement across physical systems.

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 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.

While non-Hermitian bulk systems and their sensitivity to boundary conditions have been extensively studied, how a non-Hermitian boundary affects the entanglement structure of Hermitian critical systems remains largely unexplored. Here we present a fully analytical framework by exactly solving a Hermitian gapless chain with a single non-Hermitian impurity acting as a non-Hermitian boundary. When the entanglement cut is placed at the impurity, we uncover a sharp \emph{entanglement complexification transition}: the logarithmic entanglement entropy retains its scaling form, but the effective central charge evolves from real to complex values, accompanied by a spectral collapse of the correlation matrix. We demonstrate that the real regime follows analytic continuation from a unitary defect conformal field theory (CFT), whereas the complex regime lies entirely beyond this framework. For the latter, we derive an analytical formula in perfect agreement with numerics. Our results reveal that a single non-Hermitian impurity can drive a Hermitian critical system into a nonunitary defect-CFT phase, establishing a rare analytically solvable platform for boundary non-Hermiticity.

Controlling anyon mobility is critical for robust quantum memory and understanding symmetry-enriched topological (SET) phases with subsystem symmetries (e.g., line-like, fractal, chaotic, or mixed supports). However, a unified framework for anyon mobility in SET phases with such diverse geometric patterns of symmetry supports has remained a major challenge. In this Letter, by introducing higher-order cellular automata (HOCA) -- a powerful computer science tool -- to SET physics, we establish a unified approach for complete characterization of anyon mobility induced by the complexity of subsystem symmetries. First, we design finite-depth HOCA-controlled unitary quantum circuits, yielding exactly solvable SET models with Abelian anyons and all possible locally generated subsystem symmetries. Then, we present a theorem that precisely programs all excitation mobilities (fractons, lineons, or fully mobile anyons) directly from the HOCA rule, representing the first complete characterization of anyon mobility in SET phases. As a corollary, this theorem yields symmetry-enriched fusion rules which govern mobility transmutation during fusion. Fusion rules with multiple channels are identified, exhibiting non-Abelian characteristics in Abelian anyon systems. Leveraging HOCA, this Letter opens new avenues for characterization of SET phases of matter and programmability of topological quantum codes.

Fractonic superfluids are featured by the interplay of spontaneously broken charge symmetry and mobility constraints on single-particle kinematics due to the conservation of higher moments, such as dipoles, angular charge moments, and quadrupoles. Building on prior studies by Yuan [] and Chen [], we study a class of fractonic superfluids, termed (HFS), in which bosons of multiple species interact while moment hybridization is conserved. We explore the consequences of hybridization via two model series: , conserving total moments of the same order across species, and , conserving total moments of different orders. In Model Series A, we analyze dipole moment hybridization and extend the discussion to higher-order moments, examining the ground state, Goldstone modes, correlation functions, and so on. We compute the minimal spatial dimensions, where the total charge symmetry begins to get partially broken via particle-hole condensation, leading to true off-diagonal long-range order. In Model Series B, we focus on HFS with hybrid dipole-quadrupole conservation. For both series, we introduce Bose-Hubbard–type lattice models that reduce to either of both series in the weak Hubbard interaction regime. We perform a mean-field analysis on the global phase diagram and discuss experimental realizations in strongly tilted optical lattices via a third-order perturbation theory. This work, alongside prior studies, completes a trilogy on fractonic superfluids, uncovering symmetry-breaking physics emerging from higher moment conservation, leaving various promising studies for future investigation.

In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes, despite the absence of anyons. Our understanding of these topological data remains less mature compared to 3D, where anyons have been extensively studied and can be fully described through diagrammatic representations. Inspired by recent advancements in field theory descriptions of higher-dimensional topological orders, this paper systematically constructs diagrammatic representations for 4D and 5D topological orders described by BF theory, generalizable to higher dimensions. We introduce elementary diagrams for fusion and shrinking processes, treating them as vectors in fusion and shrinking spaces, respectively, and build complex diagrams by combining these elementary diagrams. Within these vector spaces, we design unitary operations represented by F-, ∆-, and ∆²-symbols to transform between different bases. We discover pentagon equations and (hierarchical) shrinking-fusion hexagon equations that impose constraints on the legitimate forms of these unitary operations. We conjecture that the diagrammatic representations we construct apply to all anomaly-free higher-dimensional topological orders, which must satisfy these conditions and any violations indicate a quantum anomaly. This work opens promising avenues for future research, including the exploration of diagrammatic representations involving braiding and the study of non-invertible symmetries and symmetry topological field theories in higher spacetime dimensions.