TBA

• Yoshimasa Hidaka (YITP)

Lattice Study of Critical and Symmetry Breaking Phases with Categorical Symmetry

• Chenjie Wang (The University of Hong Kong)

I will present a construction of a family of 1D quantum lattice models with unitary fusion category symmetry. These models generalize the well-known anyon chain construction and can be viewed as edge theories of 2D symmetry-enriched topological states. They realize a variety of interesting phases, including gapless critical phases and phases with spontaneously broken categorical symmetries. A particularly interesting phase is an antiferromagnet-like phase in which both translation and category symmetry are broken but certain combined symmetries remain intact. However, it differs fundamentally from the conventional antiferromagnet because the associated magnetic domain walls are non-invertible. I will also briefly discuss the representative phase transitions, including gapped-to-gapless or gapless-to-gapless transitions.

Universal decay of mutual information and conditional mutual information in gapped quantum phases of matter

• Liujun Zou (National University of Singapore)

Mutual information (MI) and conditional mutual information (CMI) are central tools to characterize the correlation and entanglement in quantum systems. However, their universal properties in quantum many-body systems were poorly understood before. In this talk, I will present our recent rigorous results on the universal properties of MI and CMI in gapped quantum matter, and discuss their interesting applications. Our central theorems state that, for local spin and fermionic systems in any spatial dimension, the super-polynomial decay behavior of MI and CMI is a universal property of gapped quantum phases, i.e., all systems in such a phase possess this property if one system in this phase possesses this property. Moreover, I will explain that the MI and CMI indeed decay superpolynomially in most (if not all) known topological phases, which leads to interesting implications on how to dynamically prepare anyons and how symmetries act on topological phases.

TBA

• Jong Yeon Lee (University of Illinois Urbana-Champaign)

TBA

• Jung Hoon Han (Sungkyunkwan University)

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• Seishiro Ono (ISSP)

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• Shuhei Ohyama (RIKEN)

Topological Order in Three Spatial Dimensions and Beyond: Continuum Topological Field Theory, Diagrammatics, and Microscopic Constructions

• Peng Ye (Sun Yat-sen University)

Topological orders in three spatial dimensions and beyond can support spatially extended excitations, such as loops and membranes. These excitations give rise to exotic topological phenomena that have no direct counterparts in two-dimensional anyon systems. In this talk, I will give an overview of recent progress on higher-dimensional topological order, with a focus on continuum topological field theory, diagrammatic representations, and microscopic lattice constructions. I will discuss how field-theoretical data such as fusion, shrinking, and braiding can be formulated in field theory, represented by diagrammatics, and, in certain cases, realized explicitly in microscopic models. The most recent reference along this line is arXiv:2512.21148.

TBA

• Simeon Hellerman (Kavli IPMU)

TBA

• Naoki Yamamoto (Keio University)

Topological structure of sigma models

• Kazuya Yonekura (Tohoku University)

I will discuss general topological structure of sigma model actions which are useful for both actions and sigma model anomalies. Modulo continuous deformations, those terms are classified by the Anderson dual of bordism. If time permits, I will also discuss generalization of sigma models by combining symmetries in a nontrivial way.

TBA

• Zhicheng Yang (Peking University)

TBA

• Meng Cheng (Yale University)

Transport and puzzle of the old SU(2) anomaly at finite temperature

• Nick Poovuttikul (Chulalongkorn University)

I will give a brief overview on the method on how to extract the the anomaly induced transport coefficients of finite temperature/density QFT starting from the bordism group and mapping torus that governed its global anomaly. After that, I will focus on the puzzling case of SU(2) anomaly where the anomaly matching forbid a naive analytic continuation of DC conductivities and enforce nontrivial analytic structure of 2-point correction functions

Random Local Stabilizer Codes in Three Dimensions without String or Self-Similar Fractal Logical Operators

• Han Yan (The University of Tokyo)

Quantum error-correcting codes (QECs) are essential components of quantum computation and have deep connections to quantum phases of matter. A key obstruction to passive self-correcting QECs is the presence of string logical operators, which can generate logical errors through constant-energy-barrier processes. Haah's Codes (fracton codes) showed that three-dimensional stabilizer codes can forbid such string logical operators, but their translation-invariant structure supports self-similar fractal logical operators with a logarithmic energy barrier. We introduce the qutrit random cubic codes, a family of local qutrit Calderbank-Shor-Steane stabilizer Hamiltonians with similar cube-check structure as Haah's Code 1 but built from spatially varying stabilizers. We prove that these models retain the no-string property and numerically observe that they have properties distinct from translation-invariant fracton codes: the smallest ground-state degeneracy exponent is k=2 for odd L and k=4 for even L; noncontractible plane-logical operators span the entire logical space; and charge-push diagnostics show that the self-similar fractal operators are absent. These results demonstrate that constrained randomness can fundamentally change the nature of stabilizer codes and improve their self-correction properties. They further point to broader families of quantum error-correcting codes and quantum phases beyond canonical topological and fracton orders.

TBA

• Masaru Hongo (Niigata Universiity)

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• Chang-Tse Hsieh (National Taiwan University)

TBA

• Kantaro Ohmori (RIKEN iTHEMS)

Classifying Finite-Temperature Phases Beyond Symmetry Breaking

• Haruki Watanabe (The Hong Kong University of Science and Technology)

The classification of phases of matter at finite temperature has traditionally rested on Landau's paradigm of spontaneous symmetry breaking and local order parameters. At absolute zero, this paradigm has been decisively enlarged over the past decades: topologically ordered and symmetry-protected topological phases sharply distinguish ground states that share exactly the same symmetries. Most of these topological distinctions, however, are defined strictly at zero temperature, and whether equally sharp, symmetry-free distinctions can persist at finite temperature remains far less understood. In this talk, I address this question through two contrasting spin models. The first is the spin-1 spin ice on the pyrochlore lattice, which also serves as an effective model for the hydrogen-bond network of high-pressure water ice. Combining exact duality mappings—onto 3D $XY$ and Ising loop-gas models—with Monte Carlo simulations, I show that the topological phase transitions present at zero temperature are immediately rounded into continuous crossovers at any finite temperature, because thermally excited point-like monopoles screen the emergent gauge field. This naturally explains why molecular ice-VII and symmetric ice-X, which share identical crystal symmetry, are connected by a crossover rather than a genuine phase transition. The second model is the 3D $\mathbb{Z}_2$ toric code in a generic magnetic field, in which every higher-form symmetry is explicitly broken. In sharp contrast to the spin ice, here the topological order survives up to a genuine finite-temperature phase transition. The protection is purely geometric: the Bianchi identity forbids point-like magnetic monopoles and forces flux to proliferate only through closed loops. Using large-scale quantum Monte Carlo, I show that the topological entanglement entropy stays quantized at $\ln 2$ throughout this phase. This quantity, however, is notinvariant under quasi-local channels—a constant-depth circuit can manufacture the same $\ln 2$ from a trivial product state—and therefore cannot certify the phase on its own. I then propose the decoded Wilson-loop correlation, a channel-invariant order parameter that equals $1$ in the topological phase and $0$ in the trivial phase, furnishing a genuine topological invariant of the finite-temperature, field-driven 3D toric code as a mixed (Gibbs) state. Taken together, these examples reveal that the survival of topological order at finite temperature is dictated by the geometry of its topological excitations: point-like defects offer no protection and yield only crossovers, whereas loop-like defects can sustain a sharp phase distinction that breaks no symmetry—one captured by an appropriately constructed channel invariant.

Gaplessness of charge- and neutral-excitations under Lieb-Schultz-Mattis constraints

• Yasuhiro Tada (Hiroshima University)

We study gaplessness in one-dimensional quantum many-body systems with U(1) and translation symmetries under Lieb–Schultz–Mattis (LSM)–type constraints. While the LSM theorem imposes strong restrictions on the low-energy spectrum, the relation between charge- and neutral-excitations remains nontrivial in general interacting systems. In this work, we show that, under physically reasonable conditions and in the presence of LSM-type constraints, the absence of a neutral gap implies the absence of a charge gap. Our approach is based on a dynamical construction using local twist operations combined with Lieb–Robinson bounds, which allows us to extract quasi-local excitations carrying finite quantum numbers with vanishing excitation energy. Our results provide a unified perspective on gaplessness constrained by symmetry and filling, and suggest a general framework to diagnose gapless phases beyond specific models.

An algorithm to generate two-dimensional critical lattice models using competing anyon condensation

• Yu Zhao (Fudan University)

The critical behaviour at a second-order phase transition is often described by a conformal field theory. The restrictions imposed by conformal symmetry give rise to a number of important theoretical techniques that have made these theories central to the understanding of critical phenomena. However, efforts to classify conformal field theories have run into the challenge of identifying lattice models that have a corresponding critical point. Here, we introduce an algorithm that we call a conformal field theory factory for methodically generating two-dimensional lattice models that would flow to conformal field theories in the infrared limit. We realise these lattice models by engineering the boundary conditions of three-dimensional topological orders described by string-net models. The critical points are induced by a commensurate condensation of non-commuting anyons. Our structured method generates an infinite family of critical lattice models, including previously unknown critical points. We recover known conformal field theories that preserve the Haagerup symmetries and identify three further candidate theories. The critical couplings of our models are precisely encoded in algebraic data associated with the string-net models, thereby establishing a scheme for discovering and potentially classifying conformal field theories. Relevant references: [arXiv:2506.05324][1]. [1]: https://doi.org/10.48550/arXiv.2506.05324

TBA

• Koichi Hattori (Zhejiang University)

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• Jing-Yuan Chen (Institute for Advanced Study Tsinghua University)

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• Gil Young Cho (KAIST)

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• Yuji Hirono (Tsukuba University)

Quantum Geometry in Fractional Quantum Hall

• Dung Nguyen (Institute For Interdisciplinary Research in Science and Education, Quy Nhon, Vietnam)

I will present an effective field theory for higher-spin chiral collective modes in fractional quantum Hall states, constructed on the basis of the guiding-center (W∞) algebra. The low-energy excitations are described as area-preserving deformations of the quantum Hall fluid, forming a hierarchy of chiral modes that includes the spin-2 graviton and higher-spin excitations. The report derives the effective action governing these modes, analyzes spin mixing at finite momentum, and demonstrates that the spin-2 sector admits a geometric description on a Kähler manifold. This provides a unified theoretical framework connecting W∞ symmetry, quantum geometry, and the bimetric description of the fractional quantum Hall effect.

Discussion