Developments on Generalized Symmetries of Quantum Systems

12 May 2026, 04:30 → 14 May 2026, 21:10 Europe/Madrid

Aulario de la Merced (Universidad de Murcia)

This workshop is devoted to cutting-edge developments in the study of generalized symmetry structures in quantum systems. The notion of symmetry is one of the backbones of the theoretical analysis of quantum dynamics. In the past few years, the textbook notion of global symmetry has been vastly generalized to incorporate richer structures, including higher-form and higher-group symmetries, non-invertible symmetries, categorical symmetries, subsystem symmetries, and more. The aim of this workshop is to bring together experts on various facets of this research area, connecting with quantum field theory, string theory, quantum information theory.

Registration to the workshop is now open.

Registration is moderated. The registration fee is EUR 170.00. It includes participation in the workshop, social dinner, coffee breaks. Confirmed registered participants will receive an email notification about payment methods. In the registration form, prospective participants can indicate whether they would like to contribute a talk or a gong show/poster session presentation.

 

Invited speakers:

• Fabio Apruzzi (U. Padua and INFN, Padua)
• Francesco Benini (SISSA, Trieste)
• Po-Shen Hsin (King's Coll. London)
• Diego Rodriguez-Gomez (Oviedo U.)
• Germán Sierra (Madrid, IFT)
• Luigi Tizzano (CERN)

 

Organizing committee:

• Federico Bonetti (Murcia U.)
• José Juan Fernández-Melgarejo (Murcia U.)
• Emilio Torrente-Lujan (Murcia U.)

 

Acknowledgements

Este congreso 22891/OC/25 está financiado por la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia con cargo al Programa Regional de Movilidad, Colaboración e Intercambio de
Conocimiento "Jiménez de la Espada."

 

    

AULARIO DE LA MERCED (Planta Baja).pdf

Tuesday 12 May

09:40 → 10:00 Registration

10:00 → 11:00 Talks

10:00 Entanglement Asymmetry for Higher and Noninvertible Symmetries

Abstract

Entanglement asymmetry is a measure of symmetry breaking in quantum
subsystems, inspired by quantum information theory, particularly
suited to study out-of-equilibrium states. In the first part of the
talk I will overview this new observable, highlighting some of the key
phenomena it captures, and presenting computations in conformal field
theory. In the second part of the talk I will describe how to define
and compute the asymmetry for higher and noninvertible (or
categorical) symmetries, how it can detect spontaneous symmetry
breaking, and the role played by boundary conditions.

Speaker: Francesco Benini (SISSA, Trieste)

11:00 → 11:30 Coffee Break

11:30 → 13:10 Talks

11:30 Entropic order parameters and topological holography

Abstract

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken symmetries. Various examples of group and non-invertible symmetries are studied. In particular, the origin of the distinguishability of the vacua resulting from spontaneously broken non-invertible symmetries is made manifest with an information-theoretic perspective, where certain operators in the SymTFT are excluded from observation.

Speaker: Javier Molina-Vilaplana (Cartagena Politecnica U.)

12:30 Higher-form entanglement asymmetry

Abstract

Entanglement asymmetry is a relative entropy that faithfully diagnoses symmetry breaking in quantum states, possibly within a spatial subregion. In this work, we extend such framework to higher-form symmetries and compute entanglement asymmetry in theories with spontaneously-broken continuous zero- and higher-form symmetries. One of our central results is an entropic Coleman-Mermin-Wagner theorem, for 0- and p-form symmetries, valid also on subregions, which forbids spontaneous breaking of continuous p-form symmetries in spacetime dimensions $d\leq p+2$. Our theorem not only qualifies symmetry breaking, it also quantifies it: spontaneous breaking triggers a nonvanishing entanglement asymmetry that grows monotonically towards the infrared, and counts the number of Goldstone fields. Along the way, we derive standalone results concerning the entanglement entropy and asymmetry of Goldstone bosons and gauge fields. In particular, we find a closed-form expression for the Rényi asymmetries of a compact scalar field on spherical subregions in three and four spacetime dimensions, and for higher-form gauge fields in higher dimensions.

Speaker: Eduardo García-Valdecasas (SISSA, Trieste)

13:10 → 15:00 Lunch Break

15:00 → 16:00 Talks

15:00 Automorphism is All You Need: Transversal Non-Clifford Gates in 2+1D and Higher Symmetries from Automorphism

Abstract

We study automorphism in twisted gauge theories and discover they can give rise to generalized symmetries such as higher group and/or non-invertible symmetries. Using the automorphism symmetry, we discover transversal non-Clifford logical gates such as T gate in Clifford stabilizer models in 2+1D as well as CCZ gate in 5+1D self correcting non-Abelian quantum memory. The talk is based on works with Ryohei Kobayashi (Institute for Advanced Study) and Guanyu Zhu (IBM): https://arxiv.org/abs/2511.15783

Speaker: Po-Shen Hsin (King's College London)

16:00 → 16:30 Coffee Break

16:30 → 17:50 Talks

16:30 Categorical symmetries in tensor network algorithms

Abstract

Tensor networks give a very natural representation of systems with generalised symmetries, where the symmetry is described by a unitary fusion category. This talk will define in simple terms what those symmetries are, and how they are represented on discrete quantum systems (often spin systems) using tensor networks. Additionally, I will explain how to use those special tensor networks in algorithms, thus creating a link between abstract categorical symmetries and tangible methods of computing observables. I will comment on the relation of this topic to phase transitions and symmetry breaking.

Speaker: Weronika Wiesiolek (Cambridge U., DAMTP)

17:10 Spontaneous quantum turbulence via U(1) symmetry-breaking phase transition in a Bose gas

Abstract

The Kibble-Zurek mechanism (KZM) predicts the spontaneous formation of topological defects in a continuous phase transition driven at a finite rate. We propose the generation of spontaneous quantum turbulence (SQT) via the KZM during Bose-Einstein condensation induced by a thermal quench. Using numerical simulations of the stochastic projected Gross-Pitaevskii equation in two spatial dimensions, we describe the formation of a newborn Bose-Einstein condensate proliferated by quantum vortices. We establish the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy.

Speaker: Seong-Ho Shinn (University of Luxembourg)

Wednesday 13 May

10:00 → 11:00 Talks

10:00 SymTFT for spacetime symmetries

Abstract

I will describe a proposal for a Symmetry Topological Field Theory (SymTFT) for continuous spacetime symmetries. For a d-dimensional theory, this is formulated as a (d+1)-dimensional BF theory for the spacetime symmetry group, with Chern–Simons terms in even d that encode conformal and gravitational anomalies. Focusing in particular on conformal symmetry, I will discuss boundary conditions, how this framework captures symmetry breaking, and the resulting dilaton action. I will also show how topological defects in the SymTFT implement spacetime symmetry transformations on the boundary.Finally, I will comment on connections to gravity and holography, focusing on the truncation to the topological sector of four-dimensional gravity in the d = 3 case.

Speaker: Fabio Apruzzi (U. Padua, Dept. Phys. Astron. and INFN, Padua)

11:00 → 11:30 Coffee Break

11:30 → 13:10 Talks

11:30 Non-BPS branes as holographic symmetry operators

Abstract

In the modern approach, symmetries are described by a sector of topological defects within a quantum system. This begs the natural question, with potential far reaching implications for quantum gravity, about the holographic description of symmetries within this paradigm. In this talk we will review recent developments in this direction, specially for continuous symmetries. We will propose that holographic symmetry operators are described by non-BPS branes, and explore several consequences, implications and applications of this proposal. We will also propose an embedding of the symTFT in holography.

Speaker: Diego Rodríguez-Gómez (Oviedo U.)

12:30 Non-Abelian Continuous Symmetries and Branes in Holography

Abstract

We study topological operators that generate continuous symmetries in the context of holography. We show that such operators can be universally modeled as solitonic branes in the supergravity bulk, whose ends are anchored on the conformal boundary with a finite separation. This holographic realization mirrors the field-theoretic regularization of symmetry operators in terms of objects with finite thickness and tension. We further discuss how these objects measure the charge of Wilson lines ending on the boundary. Despite sharing similar low-energy physics, the top-down descriptions of such hanging branes generally differ, depending on the UV completion of the bulk theory, and on the geometric origins of the symmetries involved. We provide systematic prescriptions for constructing the hanging branes as certain bound states in Type IIB string theory and M-theory setups.

Speaker: Enoch Leung (Leipzig, Max Planck Inst.)

13:10 → 15:00 Lunch Break

15:00 → 16:00 Talks

15:00 Kramers-Wannier duality, non-invertible symmetries and All That

Abstract

Kramers–Wannier duality is one of the central ideas in statistical mechanics, relating the high- and low-temperature phases of the Ising model and leading to the exact determination of the critical point. In recent years, it has also emerged as a prototype of a non-invertible symmetry.

In this talk we revisit the duality of the quantum Ising chain from a modern perspective, showing how the Kramers–Wannier transformation can be interpreted as a non-invertible “half-step” translation symmetry. We then connect this picture with the conformal blocks and fusion rules of the critical Ising conformal field theory, leading to a fractionalized description of the Ising spin degrees of freedom. These ideas reveal deep links between generalized symmetries, anyons, conformal field theory and tensor-network wave functions

Speaker: Germán Sierra (Madrid U.)

16:00 → 16:30 Coffee Break

16:30 → 19:10 Talks

16:30 Gapless exotic-foliated dual models and their duality defects

Abstract

We construct Symmetry Topological Field Theories (SymTFTs) for continuous subsystem symmetries, which are inherently non-Lorentz-invariant. Our framework, which we call Mille-feuille, produces two dual bulk descriptions -- gapped foliated and exotic -- that generate gapless boundary theories via interval compactification. In this way, we obtain foliated dual realizations of various models, including the 3-dimensional XY plaquette and the 4-dimensional XYZ cube. Moreover, for these models, we construct codim-1 condensation defects by higher gauging the non-compact symmetry of the bulk with discrete torsion. These condensation defects realize non-invertible self-duality symmetries at any value of the couplings. In particular, for the XY-plaquette, this symmetry is a non-invertible continuous SO(2). Based on cond-mat.str-el/2504.11449 and hep-th/2602.03926.

Speaker: Salvatore Mancani (Padua U.)

17:10 Emergent Hamiltonians from boundary symmetries

Abstract

We introduce a systematic framework to obtain emergent local, commuting Hamiltonians in (d+1) dimensions from abelian symmetries living on a d-dimensional boundary. Starting from a generic d-dim globally symmetric system, we iteratively gauge its abelian symmetry, thereby introducing layers of gauge fields carrying dual symmetries that can themselves be gauged again. The fixed points of this iterative gauging procedure define (d+1)-dim stabilizer Hamiltonians from the local “Gauss law” constraints encoding the emergent bulk order while realizing the original symmetry in the boundary. It will be explained how this construction in 1D reproduces familiar 2D topological codes such as the toric code model, and naturally realizes all gapped boundary conditions as different 1D symmetric phases at the boundary. The framework, akin to a lattice SymTFT construction, is extended to higher-form and subsystem symmetries in any dimension, yielding for example to foliated and fractal type-I fracton 3D models.

Speaker: José Garre-Rubio (Madrid, IFT)

20:15 → 22:15 Social Dinner

Thursday 14 May

10:00 → 11:00 Talks

10:00 Symmetry Tools for Soft Theorems

Abstract

In this talk, I will explain how leading soft photon theorems in QED can be understood from the perspective of generalized global symmetries. Using HQET and SCET, the soft sector is described by Wilson lines for massive and massless charged particles, making an emergent electric 1-form symmetry manifest. I will then show that this symmetry enhances to an infinite-dimensional algebra of charges. The corresponding Ward identity reproduces Weinberg’s soft photon theorem, making contact with the asymptotic symmetry interpretation of soft theorems. Finally, I will discuss extensions of this perspective to inclusive observables.

Speaker: Luigi Tizzano (CERN)

11:00 → 11:30 Coffee Break

11:30 → 13:40 Talks

11:30 Global Aspects of 3-Form Fields in Axion Yang-Mills Systems

Abstract

Generalized symmetries have proved crucial for understanding quantum fields. In this talk, I highlight the role of higher-form symmetries within the axion Yang-Mills theory. This system exhibits an emergent 2-form symmetry, which must be gauged to satisfy certain 't Hooft anomaly matching conditions. The resulting 3-form gauge theory provides a compelling description of the infrared dynamics of axion domain walls. It also captures the interplay between the light axion and the heavier hadronic degrees of freedom. Time permitting, I will discuss how the global structure of the ultraviolet gauge group determines whether the system supports an IR fractional quantum Hall state on the axion domain walls.

Speaker: Mohamed M. Anber (Durham U., CPT)

12:30 Gauge theories for fractons and Carroll symmetries

Abstract

Effective models for fracton gauge fields can be constructed by gauging extensions of the Aristotelian algebra that include an Abelian charge and its associated dipole moment. Alternatively, such gauge theories can be obtained from Cosserat elasticity via dualization. Using the relation between dipole preserving symmetries and Carrollian algebras, these models can be generalized to describe higher-rank gauge fields that naturally couple to line-like fracton excitations, or fracton strings.

Speaker: Patricio Salgado-Rebolledo