arXiv subjects

Luisa Eck

Publications and source records attributed to Luisa Eck.

9 recordsLinked to original sources

arXiv2026

Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions

Recently, a generalized Landau paradigm has been proposed, in which a broad class of "unconventional" phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries. How to extract the universal dynamical properties of the transitions from this understanding? In this paper, we follow the Ginzburg-Landau philosophy and develop a field-theoretic description of such critical points in terms of the fluctuations of local order parameters, now of non-invertible symmetries. The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters from the Lagrangian algebra of a (2+1)D topological order. We illustrate the key ideas and the full steps of this generalized Ginzburg-Landau procedure using the transitions between gapped phases with a simple non-invertible symmetry --- the Rep($S_3$) symmetry.

cond-mat.str-el↗

arXiv2026

Non-invertible symmetry enriched string net topological orders

We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques.

cond-mat.str-el↗

arXiv2026

3d Conformal Field Theories via Fuzzy Sphere Algebra

Fuzzy sphere models conjecturally realize 3d CFTs in small systems of spinful fermions, but why they work so well is still not fully understood. Their Hamiltonians are built from electron density operators projected to the lowest Landau level. We analyze the Lie algebra generated by these density modes and its large-$s$ limits. Depending on how the limit is taken, the algebra approaches either the Girvin-MacDonald-Platzman algebra in a local planar limit or a semiclassical algebra for low-angular-momentum modes in a global commutative limit. With an additional restriction to a low-excitation sector above the paramagnetic state, the density modes become approximate harmonic oscillators. We also test whether the conformal algebra $so(3,2)$ can be realized directly by density modes. Such a representation exists only in the minimal two-electron system; its natural coproduct extension does not match the physical thermodynamic limit of a single growing fuzzy sphere.

cond-mat.str-el↗

arXiv2025

Dualities between 2+1d fusion surface models from braided fusion categories

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 $\mathcal{M} \neq \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones.

cond-mat.str-el↗

arXiv2024

Generalizations of Kitaev's honeycomb model from braided fusion categories

Fusion surface models, as introduced by Inamura and Ohmori, extend the concept of anyon chains to 2+1 dimensions, taking fusion 2-categories as their input. In this work, we construct and analyze fusion surface models on the honeycomb lattice built from braided fusion 1-categories. These models preserve mutually commuting plaquette operators and anomalous 1-form symmetries. Their Hamiltonian is chosen to mimic the structure of Kitaev's honeycomb model, which is unitarily equivalent to the Ising fusion surface model. In the anisotropic limit, where one coupling constant is dominant, the fusion surface models reduce to Levin-Wen string-nets. In the isotropic limit, they are described by weakly coupled anyon chains and are likely to realize chiral topological order. We focus on three specific examples: (i) Kitaev's honeycomb model with a perturbation breaking time-reversal symmetry that realizes chiral Ising topological order, (ii) a $\mathbb{Z}_N$ generalization proposed by Barkeshli et al., which potentially realizes chiral parafermion topological order, and (iii) a novel Fibonacci honeycomb model featuring a non-invertible 1-form symmetry.

cond-mat.str-el↗

arXiv2024

From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects

Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy.

cond-mat.stat-mech↗

arXiv2023

If your data distribution shifts, use self-learning

We demonstrate that self-learning techniques like entropy minimization and pseudo-labeling are simple and effective at improving performance of a deployed computer vision model under systematic domain shifts. We conduct a wide range of large-scale experiments and show consistent improvements irrespective of the model architecture, the pre-training technique or the type of distribution shift. At the same time, self-learning is simple to use in practice because it does not require knowledge or access to the original training data or scheme, is robust to hyperparameter choices, is straight-forward to implement and requires only a few adaptation epochs. This makes self-learning techniques highly attractive for any practitioner who applies machine learning algorithms in the real world. We present state-of-the-art adaptation results on CIFAR10-C (8.5% error), ImageNet-C (22.0% mCE), ImageNet-R (17.4% error) and ImageNet-A (14.8% error), theoretically study the dynamics of self-supervised adaptation methods and propose a new classification dataset (ImageNet-D) which is challenging even with adaptation.

cs.CV↗

arXiv2023

Critical lines and ordered phases in a Rydberg-blockade ladder

Arrays of Rydberg atoms in the blockade regime realize a wealth of strongly correlated quantum physics, but theoretical analysis beyond the chain is rather difficult. Here we study a tractable model of Rydberg-blockade atoms on the square ladder with a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry and at most one excited atom per square. We find $D_4$, $\mathbb{Z}_2$ and $\mathbb{Z}_3$ density-wave phases separated by critical and first-order quantum phase transitions. A non-invertible remnant of $U(1)$ symmetry applies to our full three-parameter space of couplings, and its presence results in a larger critical region as well as two distinct $\mathbb{Z}_3$-broken phases. Along an integrable line of couplings, the model exhibits a self-duality that is spontaneously broken along a first-order transition. Aided by numerical results, perturbation theory and conformal field theory, we also find critical Ising$^2$ and three-state Potts transitions, and provide good evidence that the latter can be chiral.

cond-mat.str-el↗

arXiv2020

Improving robustness against common corruptions by covariate shift adaptation

Today's state-of-the-art machine vision models are vulnerable to image corruptions like blurring or compression artefacts, limiting their performance in many real-world applications. We here argue that popular benchmarks to measure model robustness against common corruptions (like ImageNet-C) underestimate model robustness in many (but not all) application scenarios. The key insight is that in many scenarios, multiple unlabeled examples of the corruptions are available and can be used for unsupervised online adaptation. Replacing the activation statistics estimated by batch normalization on the training set with the statistics of the corrupted images consistently improves the robustness across 25 different popular computer vision models. Using the corrected statistics, ResNet-50 reaches 62.2% mCE on ImageNet-C compared to 76.7% without adaptation. With the more robust DeepAugment+AugMix model, we improve the state of the art achieved by a ResNet50 model up to date from 53.6% mCE to 45.4% mCE. Even adapting to a single sample improves robustness for the ResNet-50 and AugMix models, and 32 samples are sufficient to improve the current state of the art for a ResNet-50 architecture. We argue that results with adapted statistics should be included whenever reporting scores in corruption benchmarks and other out-of-distribution generalization settings.

cs.LG↗