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arXiv:2605.13961

A Twist on Scattering from Defect Anomalies

Andrea Antinucci, Christian Copetti, Giovanni Galati, Giovanni Rizi

Published May 13, 2026• 0 citations
arXivHTMLPDF

Abstract

In the presence of extended defects, familiar incoming particles can scatter into exotic outgoing states created by twist operators. We show that one possible mechanism driving these "categorical scattering" processes is the presence of localized 't Hooft anomalies on the defect's worldvolume. Defect anomalies trap non-trivial charges at junctions between the symmetry lines and the interface, opening new transmission channels that would naively appear to violate selection rules. After outlining the general mechanism, we investigate several concrete examples with defects, interfaces, and boundaries. For models of massless chiral fermions already studied in the literature, we show that the emergence of twist operators can be understood as a consequence of defect anomalies. We then introduce new massive integrable theories in which a similar phenomenon occurs, and we explicitly solve the associated scattering problem, obtaining new integrable solutions. Finally, we construct lattice spin chains with defects where similar physics is expected to arise.

DOI
10.48550/arxiv.2605.13961

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In the presence of extended defects, familiar incoming particles can scatter into exotic outgoing states created by twist operators. We show that one possible mechanism driving these "categorical scattering" processes is the presence of localized 't Hooft anomalies on the defect's worldvolume. Defect anomalies trap non-trivial charges at junctions between the symmetry lines and the interface, opening new transmission channels that would naively appear to violate selection rules. After outlining the general mechanism, we investigate several concrete examples with defects, interfaces, and boundaries. For models of massless chiral fermions already studied in the literature, we show that the emergence of twist operators can be understood as a consequence of defect anomalies. We then introduce new massive integrable theories in which a similar phenomenon occurs, and we explicitly solve the associated scattering problem, obtaining new integrable solutions. Finally, we construct lattice spin chains with defects where similar physics is expected to arise.
Non-Abelian excitations are sought after because of the promise they hold for topological quantum computation. However, in spite of many proposals of systems in which they can occur intrinsically, observation has proved to be elusive. In this thesis, we study ways in which we can engineer such excitations by combining two parent Abelian theories, and as a result allow for defects which host non-Abelian zero modes. We first formulate the symmetries of the anyonic excitations of Abelian topological states. Then, we study properties of semiclassical point defects, called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. Non-Abelian twist defects appear between different gapped phases. We study the twist defects for a variety of bosonic ADE fractional quantum spin Hall systems for which the anyonic symmetries turn out to be given by their Dynkin diagrams. We also look at superconducting heterostructures with fermionic quantum Hall states and show the presence of anyonic symmetries and twist defects which physically correspond to a fermion parity flip. This can result in Majorana bound states at such defects instead of more exotic parafermions as was believed before. This is because the presence of the superconductor necessitates the consideration of a larger bosonic topological order. We then investigate the twist defects further by promoting the anyonic symmetries from global to local. This deconfines the defects and results in non-Abelian topological states called twist liquids. Finally, we study the emergence of new topological order from two constituent systems driven by the condensation of a composite boson. This allows us to study a variety of systems with non-Abelian excitations.
A bstract We explore the dynamics of the fermion-rotor system, a simple impurity model in d = 1 +1 dimensions consisting of a collection of purely right-moving fermions interacting with a quantum mechanical rotor localised at the origin. This was first introduced by Polchinski as a toy model for monopole-fermion scattering and is surprisingly subtle, with ingoing and outgoing fermions carrying different quantum numbers. We show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries. We further show how generalisations of this model with multiple rotors and unequal charges can be viewed as a UV-completion of boundary states for chiral theories, including the well-studied 3450 model. We compute correlation functions between ingoing and outgoing fermions, and show that fermions dressed with the rotor degree of freedom act as local operators and create single-particle states, generalizing an earlier result obtained in a theory with a single rotor and equal charges. Finally, we point out a mod 2 anomaly in these models that descends from the Witten anomaly in 4d.
't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by ∼a1∧a2∧a3∧a4\sim a_1\wedge a_2\wedge a_3\wedge a_4∼a1​∧a2​∧a3​∧a4​, where the aia_iai​ denote background gauge fields for the global symmetries. Through explicit lattice gauging, we demonstrate the emergence of higher symmetry structures, including 2-group, non-invertible, and higher fusion categorical symmetries. We also provide a field-theoretical understanding of these results. Applying this framework to systems with Lieb-Schultz-Mattis anomalies, obtained by promoting part of the internal symmetries to translational symmetries, we demonstrate that modulated (dipole) symmetries arise as direct counterparts of those in systems with purely internal typeIV anomalies. Importantly, we uncover a qualitatively new feature absent in previously studied modulated symmetries: their realization can become intrinsically defect-dependent. In particular, the emergent symmetry structure changes depending on whether symmetry defects are present. This work establishes a concrete lattice realization of mixed anomalies and reveals a rich structure of emergent symmetries, thereby clarifying their role in constraining quantum phases of matter.
Monodromy defects describe a dynamical termination of topological symmetry operators, and are sourced by a localized background magnetic flux. We study their properties in gapped SPT phases and, by inflow, in gapless theories with an anomalous symmetry. The background flux acts as a source for the anomaly, impacting the definition of the monodromy defect, which can only be defined as a domain wall between the symmetry generator and a topological order induced by the anomaly. The topological dressing has several consequences, such as the presence of protected chiral edge modes on the defect's worldvolume, and the adiabatic pumping of gapless degrees of freedom bound to the localized flux. We verify our predictions in several examples, focusing on monodromy defects for anomalous chiral symmetries, both in the continuum and on the lattice.
We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1)) H 3 ( G , U ( 1 ) ) × H 2 ( G , U ( 1 ) ) . The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.
Abstract In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations , cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.