Publications

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Instanton density operator in lattice QCD from higher category theory

Jing-Yuan Chen

SciPost Phys. 19, 158 (2025) · published 17 December 2025 | · pdf

A natural definition for instanton density operator in lattice QCD has long been desired. We show this problem is, and has to be, solved by higher category theory. The problem is solved by refining at a conceptual level the Yang-Mills theory on lattice, in order to recover the homotopy information in the continuum, which would have been lost if we put the theory on lattice in the traditional way. The refinement needed is a generalization—through the lens of higher category theory—of the familiar process of Villainization that captures winding in lattice XY model and Dirac quantization in lattice Maxwell theory. The apparent difference is that Villainization is in the end described by principal bundles, hence familiar, but more general topological operators can only be captured on the lattice by more flexible structures beyond the usual group theory and fibre bundles, making the language of categories natural and necessary. The key structure we need for our particular problem is called multiplicative bundle gerbe, based upon which we can construct suitable structures to naturally define the 2d Wess-Zumino-Witten term, 3d skyrmion density operator and 4d hedgehog defect for lattice $S^3$ (pion vacua) non-linear sigma model, and the 3d Chern-Simons term, 4d instanton density operator and 5d Yang monopole defect for lattice $SU(N)$ Yang-Mills theory; moreover, the structures behind the non-linear sigma model and the Yang-Mills theory are related via an implicit Yang-Baxter equation. In a broader perspective, higher category theory enables us to rethink more systematically the relation between continuum quantum field theory and lattice quantum field theory. We sketch a proposal towards a general machinery that constructs the suitably refined lattice degrees of freedom for a given non-linear sigma model or gauge theory in the continuum, realizing the desired topological operators on the lattice.
Dualities between 2+1d fusion surface models from braided fusion categories

Luisa Eck

SciPost Phys. 19, 157 (2025) · published 17 December 2025 | · pdf

Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} ≠ \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones.
Noncommutative resolutions and CICY quotients from a non-Abelian GLSM

Johanna Knapp, Joseph McGovern

SciPost Phys. 19, 156 (2025) · published 17 December 2025 | · pdf

We discuss a one-parameter non-Abelian GLSM with gauge group $(U(1)× U(1)× U(1))\rtimes\mathbb{Z}_3$ and its associated Calabi-Yau phases. The large volume phase is a free $\mathbb{Z}_3$-quotient of a codimension $3$ complete intersection of degree-$(1,1,1)$ hypersurfaces in $\mathbb{P}^2×\mathbb{P}^2×\mathbb{P}^2$. The associated Calabi-Yau differential operator has a second point of maximal unipotent monodromy, leading to the expectation that the other GLSM phase is geometric as well. However, the associated GLSM phase appears to be a hybrid model with continuous unbroken gauge symmetry and cubic superpotential, together with a Coulomb branch. Using techniques from topological string theory and mirror symmetry we collect evidence that the phase should correspond to a non-commutative resolution, in the sense of Katz-Klemm-Schimannek-Sharpe, of a codimension two complete intersection in weighted projective space with $63$ nodal points, for which a resolution has $\mathbb{Z}_3$-torsion. We compute the associated Gopakumar-Vafa invariants up to genus $11$, incorporating their torsion refinement. We identify two integral symplectic bases constructed from topological data of the mirror geometries in either phase.
Precision calibration of calorimeter signals in the ATLAS experiment using an uncertainty-aware neural network

ATLAS Collaboration

SciPost Phys. 19, 155 (2025) · published 16 December 2025 | · pdf

The ATLAS experiment at the Large Hadron Collider explores the use of modern neural networks for a multi-dimensional calibration of its calorimeter signal defined by clusters of topologically connected cells (topo-clusters). The Bayesian neural network (BNN) approach not only yields a continuous and smooth calibration function that improves performance relative to the standard calibration but also provides uncertainties on the calibrated energies for each topo-cluster. The results obtained by using a trained BNN are compared to the standard local hadronic calibration and to a calibration provided by training a deep neural network. The uncertainties predicted by the BNN are interpreted in the context of a fractional contribution to the systematic uncertainties of the trained calibration. They are also compared to uncertainty predictions obtained from an alternative estimator employing repulsive ensembles.
Von Neumann subfactors and non-invertible symmetries

Xingyang Yu, Hao Y. Zhang

SciPost Phys. 19, 154 (2025) · published 15 December 2025 | · pdf

We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object $\mathcal{A}$ are encoded in the bipartite principal graph of a subfactor. The dual principal graph captures the quantum symmetry $\mathcal{C}'$ obtained by gauging $\mathcal{A}$ in $\mathcal{C}$, as well as a reverse gauging back to $\mathcal{C}$. From a given subfactor $N \subset M$, we derive a quiver diagram that encodes the representations of the associated non-invertible symmetry. We show how this framework provides necessary conditions for admissible gaugings, enabling the construction of generalized orbifold groupoids. To illustrate this strategy, we present three examples: Rep$(D_4)$ as a warm-up, the higher-multiplicity case Rep$(A_4)$ with its associated generalized orbifold groupoid and triality symmetry, and Rep$(A_5)$, where $A_5$ is the smallest non-solvable finite group. For applications to gapless systems, we embed these generalized gaugings as global manipulations on the conformal manifolds of $c=1$ CFTs and uncover new self-dualities in the exceptional $SU(2)_1/A_5$ theory. For $\mathcal{C}$-symmetric TQFTs, we use the subfactor-derived quiver diagrams to characterize gapped phases, describe their vacuum structure, and classify the recently proposed particle-soliton degeneracies.
A correspondence between the Rabi model and an Ising model with long-range interactions

Bruno Scheihing-Hitschfeld, Néstor Sepúlveda

SciPost Phys. 19, 153 (2025) · published 15 December 2025 | · pdf

By means of Trotter's formula, we show that transition amplitudes between a class of generalized coherent states in the Rabi model can be understood in terms of a certain Ising model featuring long-range interactions beyond nearest neighbors in its thermodynamic limit. Specifically, we relate the transition amplitudes in the Rabi model to a sum over binary variables of the form of a partition function of an Ising model with a number of spin sites equal to the number of steps in Trotter's formula applied to the real-time evolution of the Rabi model. From this, we show that a perturbative expansion in the energy splitting of the two-level subsystem in the Rabi model is equivalent to an expansion in the number of spin domains in the Ising model. We conclude by discussing how calculations in one model give nontrivial information about the other model, and vice versa, as well as applications and generalizations this correspondence may find.
Algebraic law of local correlations in a driven Rydberg atomic system

Xin Wang, XiaoFeng Wu, Bo Yang, Bo Zhang, Bo Xiong

SciPost Phys. 19, 152 (2025) · published 11 December 2025 | · pdf

Understanding the mechanism behind the buildup of inner correlations is crucial for studying nonequilibrium dynamics in complex, strongly interacting many-body systems. Here we investigate both analytically and numerically the buildup of antiferromagnetic (AF) correlations in a dynamically tuned Ising model with various geometries, realized in a Rydberg atomic system. Through second-order Magnus expansion (ME), we demonstrate quantitative agreement with numerical simulations for diverse configurations including $2 × n$ lattice and cyclic lattice with a star. We find that the AF correlation magnitude at fixed Manhattan distance obeys a universal superposition principle: It corresponds to the algebraic sum of contributions from all shortest paths. This superposition law remains robust against variations in path equivalence, lattice geometries, and quench protocols, establishing a new paradigm for correlation propagation in quantum simulators.
Sparsity in the numerical six-point bootstrap

Sebastian Harris

SciPost Phys. 19, 151 (2025) · published 10 December 2025 | · pdf

The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a six-point generalisation of the numerical bootstrap, yielding qualitatively new, rigorous bounds on CFT data. However, the numerical six-point bootstrap requires solving SDPs involving infinite-dimensional matrices, which has so far limited its applicability and hindered scalability in early implementations. This work overcomes the challenges by using sparse matrix decompositions to exploit the banded structure of the underlying SDP. The result is a rewriting of one-dimensional six-point bootstrap problems as effectively two-dimensional standard mixed correlator four-point bootstrap computations. As application, novel bounds whose extremal correlators interpolate between the six-point functions of the generalised free fermion and boson are derived. The extremal interpolations are matched with perturbative deformations of the massive free boson in AdS$_2$.
Doping lattice non-Abelian quantum Hall states

Zhengyan Darius Shi, Carolyn Zhang, Senthil Todadri

SciPost Phys. 19, 150 (2025) · published 9 December 2025 | · pdf

We study quantum phases of a fluid of mobile charged non-Abelian anyons, which arise upon doping the lattice Moore-Read quantum Hall state at lattice filling $\nu = 1/2$ and its generalizations to the Read-Rezayi ($RR_k$) sequence at $\nu = k/(k+2)$. In contrast to their Abelian counterparts, non-Abelian anyons present unique challenges due to their non-invertible fusion rules and non-Abelian braiding structures. We address these challenges using a Chern-Simons-Ginzburg-Landau (CSGL) framework that incorporates the crucial effect of energy splitting between different anyon fusion channels at nonzero dopant density. For the Moore-Read state, we show that doping the charge $e/4$ non-abelion naturally leads to a fully gapped charge-$2$ superconductor without any coexisting topological order. The chiral central charge of the superconductor depends on details of the interactions determining the splitting of anyon fusion channels. For general $RR_k$ states, our analysis of states obtained by doping the basic non-abelion $a_0$ with charge $e/(k+2)$ reveals a striking even/odd pattern in the Read-Rezayi index $k$. We develop a general physical picture for anyon-driven superconductivity based on charge-flux unbinding, and show how it relates to the CSGL description of doped Abelian quantum Hall states. Finally, as a bonus, we use the CSGL formalism to describe transitions between the $RR_k$ state and a trivial period-$(k+2)$ CDW insulator at fixed filling, driven by the gap closure of the fundamental non-Abelian anyon $a_0$. Notably, for $k=2$, this predicts a period-4 CDW neighboring the Moore-Read state at half-filling, offering a potential explanation of recent numerical observations in models of twisted MoTe$_2$.
Learning the non-Markovian features of subsystem dynamics

Michele Coppola, Mari Carmen Bañuls, Zala Lenarčič

SciPost Phys. 19, 149 (2025) · published 8 December 2025 | · pdf

The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.

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