arXiv subjects

Ryan A. Lanzetta

Publications and source records attributed to Ryan A. Lanzetta.

7 recordsLinked to original sources

arXiv2026

Cutting corners: exciting and magical bounds from the cusp bootstrap

An illuminating probe of the dynamics of a line defect is the global geometry of its worldline. For a conformal line defect in a conformal field theory, sharp corners in the worldline, i.e. cusps, host dynamical degrees of freedom characterized in part by a spectrum of scaling dimensions, called cusp anomalous dimensions. We present various general bounds on cusp anomalous dimensions following from unitarity and cutting-and-gluing consistency of different defect geometries. We first establish, for cusps involving conjugate defects, that level crossings upon varying the cusp angle are forbidden between the lightest singlet cusp and any non-singlet cusp, proving that singlet cusps are the lightest. Then, we study line defects arranged in a rectangular geometry, which are subject to bootstrap constraints reminiscent of the spinless modular bootstrap. We find an analytic ``magic" functional that produces an optimal and universal lower bound on the dimension of a right angle bare cusp in terms of the universal defect Casimir energy between the corresponding defect and its conjugate in flat space.

hep-th↗

arXiv2026

Eye-opening bounds on cusps

We derive new nonperturbative inequalities on the cusp anomalous dimensions of conformal line defects. We impose reflection positivity, locality, and conformal invariance on a pair of cusps forming an ``eye'' geometry, deriving a novel condition on the cusp anomalous dimension which we refer to as conformal concavity. The resulting constraint is much stronger than the known angular concavity, and our derivation applies also to cusps involving distinct line defects. Remarkably, it directly links the smooth and fusion limits, yielding bounds on defect-changing operator dimensions, Casimir energies, and subleading fusion data. We thus uncover a new quantitative bridge between aspects of the local operator data and the fusion rules of line operators in conformal field theories.

hep-th↗

arXiv2026

Self-dual Higgs transitions: Toric code and beyond

The toric code, when deformed in a way that preserves the self-duality $\mathbb{Z}_2$ symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the $\mathbb{Z}_2$ symmetry. Numerically, this transition was found to be continuous, which makes it particularly enigmatic given the longstanding absence of a continuum field-theoretic description. In this work we propose such a continuum field theory for the transition dubbed the $SO(4)_{2,-2}$ Chern-Simons-Higgs (CSH) theory. We show that our field theory provides a natural "mean-field" understanding of the phase diagram. Moreover, it can be generalized to an entire series of theories, namely the $SO(4)_{k,-k}$ CSH theories, labeled by an integer $k$. For each $k>2$, the theory describes an analogous transition involving different non-Abelian topological orders, such as the double Fibonacci order ($k=3$) and the $S_3$ quantum double ($k=4$). For $k=1$, we conjecture that the corresponding CSH transition is in fact infrared-dual to the $3d$ Ising transition, in close analogy with the particle-vortex duality of a complex scalar.

cond-mat.str-el↗

arXiv2026

Fortuitous Universality of Bose-Kondo Impurities

We use the fuzzy-sphere approach to study the Bose-Kondo impurity problem, namely a spin-$S$ impurity coupled to the $(2+1)$-dimensional $O(3)$ Wilson-Fisher CFT (Heisenberg universality class). We demonstrate that for $S=1/2,1,3/2$ the impurity flows to a distinct stable interacting conformal defect for each $S$. Using large-scale exact diagonalization and density-matrix renormalization group methods, we observe integer-spaced defect spectrum consistent with defect conformal symmetry and compute several low-lying defect primary operators as well as the RG monotonic $g$-function. Our findings show that despite sharing the same symmetry and anomaly, Bose-Kondo impurities flow to distinct stable infrared conformal fixed points, which we refer to as \emph{fortuitous universality}. We expect this fortuitous universality to persist for all $S$, extending to $S\rightarrow\infty$, with each spin-$S$ impurity flowing to its own stable infrared conformal fixed point.

cond-mat.str-el↗

arXiv2025

The beginning of the endpoint bootstrap for conformal line defects

A challenge in the study of conformal field theory (CFT) is to characterize the possible defects in specific bulk CFTs. Given the success of numerical bootstrap techniques applied to the characterization of bulk CFTs, it is desirable to develop similar tools to study conformal defects. In this work, we successfully demonstrate this possibility for endable conformal line defects. We achieve this by incorporating the endpoints of a conformal line defect into the numerical four-point bootstrap and exploit novel crossing symmetry relations that mix bulk and defect CFT data in a way that further possesses positivity, so that rigorous numerical bootstrap techniques are applicable. We implement this approach for the pinning field line defect of the $3d$ Ising CFT, obtaining estimates of its defect CFT data that agree well with other recent estimates, particularly those obtained via the fuzzy sphere regularization. An interesting consequence of our bounds is nearly rigorous evidence that the $\mathbb Z_2$-symmetric defect exhibiting long range order obtained as a direct sum of two conjugate pinning field defects is unstable to domain wall proliferation.

cond-mat.str-el↗

arXiv2025

Bootstrapping the Quantum Hall problem

The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study interacting electrons in the lowest Landau level by minimizing the energy as a function of the static structure factor subject to a set of constraints, bypassing the need to construct the full many-body wavefunction. This approach rigorously lower bounds the ground state energy, making it complementary to conventional variational upper bounds. We show that the lower bound we obtain is relatively tight, within at most 5\% from the ground state energy computed with exact diagonalization (ED) at small system sizes, and generally gets tighter as we include more constraints. In addition to energetics, our results reproduce the correct power law dependence of the pair correlation function at short distances and the existence of a large entanglement gap in the two-particle entanglement spectra for the Laughlin states at $ν= 1/3$. We further identify signatures of the composite Fermi liquid state close to half-filling. This shows that the bootstrap approach is capable, in principle, of describing non-trivial gapped topologically ordered, as well as gapless, phases. At the end, we will discuss possible extensions and limitations of this approach. Our work establishes numerical bootstrap as a promising method to study many-body phases in topological bands, paving the way to its application in moiré platforms where the energetic competition between fractional quantum anomalous Hall, symmetry broken, and gapless states remains poorly understood.

cond-mat.str-el↗

arXiv2022

Bootstrapping Lieb-Schultz-Mattis anomalies

We incorporate the microscopic assumptions that lead to a certain generalization of the Lieb-Schultz-Mattis (LSM) theorem for one-dimensional spin chains into the conformal bootstrap. Our approach accounts for the "LSM anomaly" possessed by these spin chains through a combination of modular bootstrap and correlator bootstrap of symmetry defect operators. We thus obtain universal bounds on the local operator content of (1+1)$d$ conformal field theories (CFTs) that could describe translationally invariant lattice Hamiltonians with a $\mathbb Z_N\times \mathbb Z_N$ symmetry realized projectively at each site. We present bounds on local operators both with and without refinement by their global symmetry representations. Interestingly, we can obtain non-trivial bounds on charged operators when $N$ is odd, which turns out to be impossible with modular bootstrap alone. Our bounds exhibit distinctive kinks, some of which are approximately saturated by known theories and others that are unexplained. We discuss additional scenarios with the properties necessary for our bounds to apply, including certain multicritical points between (1+1)$d$ symmetry protected topological phases, where we argue that the anomaly studied in our bootstrap calculations should emerge.

cond-mat.str-el↗