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arXiv:2608.21791

Critical Topological Photonics in Synthetic Dimensions

Mingyuan Chen, Yuwei Jing, Franco Nori, Xue-Jia Yu

physics.opticscond-mat.stat-mechquant-phSubmitted Aug 22, 2026• Announced Aug 25, 2026• 0 citations
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Abstract

Topological states and criticality have long been regarded as incompatible ingredients: the former requires a finite spectral gap, whereas the latter demands its closure. Guided by this view, topological photonics has focused almost exclusively on gapped phases, treating gap-closing transitions as mere phase boundaries. In this work, we propose a class of topological states in which topology coexists with criticality in experimentally accessible synthetic-frequency photonic platforms. In a one-dimensional (1D) synthetic lattice, we identify such critical topological photonic states through midgap degeneracies in the single-particle entanglement spectrum, and uncover a topology-enforced multicritical point that reorganizes the topology of neighboring critical states. We further extend this framework to two dimensions (2D). Our work provides an experimentally accessible route to critical topological photonics, and may also inspire novel applications such as critical topological sensing.

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15 pages, 9 figures. Any comments or suggestions are welcome!

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Topological states and criticality have long been regarded as incompatible ingredients: the former requires a finite spectral gap, whereas the latter demands its closure. Guided by this view, topological photonics has focused almost exclusively on gapped phases, treating gap-closing transitions as mere phase boundaries. In this work, we propose a class of topological states in which topology coexists with criticality in experimentally accessible synthetic-frequency photonic platforms. In a one-dimensional (1D) synthetic lattice, we identify such critical topological photonic states through midgap degeneracies in the single-particle entanglement spectrum, and uncover a topology-enforced multicritical point that reorganizes the topology of neighboring critical states. We further extend this framework to two dimensions (2D). Our work provides an experimentally accessible route to critical topological photonics, and may also inspire novel applications such as critical topological sensing.
Recent advances have revealed that topology can further enrich the universality classes of quantum phase transitions, thereby extending beyond the traditional paradigms of statistical and condensed matter physics. However, multicriticality between topologically distinct quantum critical lines remains insufficiently explored. In this Letter, we systematically construct and investigate a novel class of topologically enforced Lifshitz multicritical points in one dimensional chiral symmetric fermionic systems. Such multicriticality is driven solely by changes in the topology of neighboring critical lines, beyond previously recognized multicritical points that are typically induced by changes in critical exponents. More importantly, the topologically enforced multicriticality identified here can host robust topological degeneracies while surprisingly exhibiting a breakdown of the Li Haldane bulk boundary correspondence-a phenomenon we elucidate through a simple physical picture.
Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.
Recently, the intriguing interplay between topology and quantum criticality has been unveiled in one-dimensional topological chains with extended nearest-neighbor couplings. In these systems, topologically distinct critical phases emerge with localized edge modes despite the vanishing bulk gap. In this work, we study the topological multicritical points at which distinct gapped and critical phases intersect. Specifically, we consider a topological chain with coupling up to the third nearest neighbors, which shows stable localized edge modes at the multicritical points. These points possess only nontrivial gapped and critical phases around them and are also characterized by the quadratic dispersion around the gap-closing points. We characterize the topological multicritical points in terms of the topological invariant obtained from the zeros of the complex function associated with the Hamiltonian. Further, we analyze the nature of zeros in the vicinity of the multicritical points by calculating the discriminants of the associated polynomial. The discriminant uniquely identifies the topological multicritical points and distinguishes them from the trivial ones. Moreover, we identify the underlying physical mechanism in terms of kinetic inversion in higher-order terms. We finally study the robustness of the zero-energy modes at the multicritical points at weak disorder strengths, and reveal the presence of a topologically nontrivial gapless Anderson-localized phase at strong disorder strengths.
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Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in lattice realization, remains insufficiently explored. In this Letter, we reveal that certain deconfined criticality can be regarded as an intrinsically gapless topological state without gapped counterparts in a one dimensional lattice model. Using a combination of field-theoretic arguments and large-scale numerical simulations, we establish the global phase diagram of the model, which features deconfined critical lines separating two distinct spontaneous symmetry breaking ordered phases. More importantly, we unambiguously demonstrate that the mixed anomaly inherent to deconfined criticality enforces topologically robust edge modes near the boundary, providing a general mechanism by which deconfined criticality manifests as a gapless topological state. Our findings not only offer a new perspective on deconfined criticality but also deepen our understanding of gapless topological phases of matter.
Recently topological states of matter have witnessed a new physical phenomenon where both edge modes and gapless bulk coexist at topological quantum criticality. The presence and absence of edge modes on a critical line can lead to an unusual class of topological phase transition between the topological and nontopological critical phases. We explore the existence of this new class of topological phase transitions in a generic model representing the topological insulators and superconductors and we show that such transition occurs at a multicritical point, i.e., at the intersection of two critical lines. To characterize these transitions we reconstruct the theoretical frameworks, which include bound state solution of the Dirac equation, winding number, correlation factors, and scaling theory of the curvature function to work for the criticality. Critical exponents and scaling laws are discussed to distinguish between the multicritical points, which separate the critical phases. Entanglement entropy and its scaling in the real space provide further insights into the unique transition at criticality revealing the interplay between fixed point and critical point at the multicriticalities.