About

Professor Barry Bradlyn is an Associate Professor in the Department of Physics at the University of Illinois, joining the faculty in 2018. He received his bachelor's degree in Physics from the Massachusetts Institute of Technology in 2009 and completed his Ph.D. at Yale University in 2015 under the supervision of Nicholas Read. His doctoral research focused on linear response and Berry phases in the fractional quantum Hall effect, where he developed a formalism for computing viscoelastic and thermal response functions for two-dimensional topological phases. Following his Ph.D., Professor Bradlyn held a postdoctoral research position at the Princeton Center for Theoretical Science from 2015 to 2018. During this time, he studied the role of crystal symmetries in topological insulators and semimetals, predicting the existence of topologically charged, multiply degenerate fermions in weakly interacting crystals with no known analogue in high energy physics. He also developed a real-space formulation of topological band theory, enabling the prediction of many new topological insulators and semimetals. His research broadly focuses on the discovery and understanding of topological phases of matter, exploring how topological invariants distinguish different phases and lead to exotic phenomena such as quantized transport and fractional bulk excitations. His work aims to marry ideas from topology and symmetry to study new phenomena in condensed matter physics, with current research topics including the viscous and optical response of topological materials, magnetic topological materials, and symmetry-protected topological phenomena.

Research topics

• Computer Science
• Quantum mechanics
• Physics
• Mathematics
• Condensed matter physics
• Geography
• Pure mathematics
• Cartography
• Theoretical physics
• Combinatorics
• Business
• Materials science
• Biology
• Geometry
• World Wide Web

Selected publications

• Geometry of Contact Terms in Linear Response: Applications to Elasticity

  arXiv (Cornell University) · 2026-03-10

  preprintOpen accessSenior author

  Employing the Kubo linear response formalism to calculate the elasticity of anisotropic systems has been shown to yield odd elastic moduli. For Hamiltonian systems, this result seems to be contradictory as it would violate energy conservation. To resolve this discrepancy, we examine the predictions of quantum linear response in the context of our expectation from classical elasticity theory. Our framework reveals that the geometry of the space of strain perturbations introduces correction factors to the correspondence between the Kubo formula and the elastic moduli which resolves the contradiction. We use a two-dimensional gas of electrons in a magnetic field as a pedagogical example. We use generalized f-sum rules to demonstrate how contact terms may reveal themselves in experimental measurements. Finally, we discuss the implications of our results for interpreting more general linear response functions.

  PublisherDOI

• Fundamental Tests of Quantum Geometric Bounds in Ionic and Covalent Insulators using Inelastic X-Ray Scattering

  ArXiv.org · 2026-01-27

  articleOpen access

  Quantum geometry underlies many fundamental properties of materials, but it has remained largely inaccessible to direct experiment. Here we demonstrate that inelastic x-ray scattering (IXS) provides a direct, quantitative probe of quantum geometry and quantum information in solids. Studying two prototype insulators, covalently bonded diamond and ionically bonded LiF, we measure the density response and experimentally determine the quantum Fisher information, the associated Bures metric, and the electron localization length. These measurements enable a quantitative comparison of quantum geometry for two distinct bonding environments. We find that the dimensionless quantum weight, $aK(q)$, which quantifies the longitudinal localization of quantum information, is constrained by fundamental electrostatic bounds in both materials. Crucially, the quantum weight of diamond exceeds that of LiF, indicating that covalent bonds exhibit a higher degree of delocalization and higher density of quantum information than the ionic bonds. Our results establish a direct experimental relationship between quantum information, electron localization, and chemical bonding, and identify IXS as a powerful tool for measuring quantum geometry in materials.

  PublisherOA PDF

• Building blocks of topological band theory for photonic crystals

  arXiv (Cornell University) · 2026-01-09

  preprintOpen accessSenior author

  We derive a framework for classifying topological bands in three-dimensional photonic band structures, where the zero frequency polarization singularity implied by Maxwell's equations complicates the direct application of existing symmetry-based approaches. Building on recent advances in the regularization of photonic bands, we use the recently introduced concept of stable real-space invariants (SRSIs) to show how photonic band structures can be unambiguously characterized in terms of equivalence classes of band representations. We classify topologically trivial photonic bands using SRSIs, treating them as the fundamental building blocks of 3D photonic band structures. This means that if certain bands cannot be constructed from these building blocks, they are necessarily topological. Furthermore, we distinguish between photonic and electronic band structures by analyzing which SRSI values are allowed in systems with and without polarization singularity. We also explore the impact of the polarization singularity on the behavior of Wilson loops, providing new insights into the topological classification of 3D photonic systems.

  PublisherDOI

• Fundamental Tests of Quantum Geometric Bounds in Ionic and Covalent Insulators using Inelastic X-Ray Scattering

  Open MIND · 2026-01-27

  preprint

  Quantum geometry underlies many fundamental properties of materials, but it has remained largely inaccessible to direct experiment. Here we demonstrate that inelastic x-ray scattering (IXS) provides a direct, quantitative probe of quantum geometry and quantum information in solids. Studying two prototype insulators, covalently bonded diamond and ionically bonded LiF, we measure the density response and experimentally determine the quantum Fisher information, the associated Bures metric, and the electron localization length. These measurements enable a quantitative comparison of quantum geometry for two distinct bonding environments. We find that the dimensionless quantum weight, $aK(q)$, which quantifies the longitudinal localization of quantum information, is constrained by fundamental electrostatic bounds in both materials. Crucially, the quantum weight of diamond exceeds that of LiF, indicating that covalent bonds exhibit a higher degree of delocalization and higher density of quantum information than the ionic bonds. Our results establish a direct experimental relationship between quantum information, electron localization, and chemical bonding, and identify IXS as a powerful tool for measuring quantum geometry in materials.

  DOI

• Ising samples 16x16 lattice, 2d, grokking vs learning

  Zenodo (CERN European Organization for Nuclear Research) · 2026-05-01

  datasetOpen access

  Ising dataset associated with Grokking vs. Learning: Same Features, Different Encodings (arXiv:2502.01739).

  PublisherDOI

• Leggett-Garg Inequality Violations Bound Quantum Fisher Information

  ArXiv.org · 2026-04-10

  articleOpen access

  We prove that a violation of a Leggett-Garg inequality for bounded observables in stationary pure states and thermal states yields a rigorous lower bound on the quantum Fisher information. This turns a qualitative foundations test of realism in quantum systems into a quantitative witness of useful quantum sensitivity and, in the collective setting, into a lower bound on multipartite entanglement depth in many-body systems. We further demonstrate that Leggett-Garg violations are constrained by the same spectral moments, susceptibilities, and $f$-sum-rule bounds that organize many-body response. Our results show that temporal correlations of a single collective observable can serve as an experimentally accessible witness of many-body quantum coherence, without requiring full state reconstruction.

  PublisherOA PDF

• Grokking vs. Learning: Same features, different encodings

  Machine Learning Science and Technology · 2026-05-02

  preprintOpen access

  Abstract Grokking typically achieves similar losses to ordinary, `steady', learning. This work asks whether these different learning paths lead to fundamental differences in the learned models. To do so, we compare the features, compressibility, and learning dynamics of models trained via each path in two controlled toy tasks. We find that grokked and steadily trained models learn the same features, but there can be large differences in the efficiency with which these features are encoded. In particular, we find a novel `compressive regime' of steady training in which there emerges a linear trade-off between model loss and compressibility, which is absent in grokking. In this regime, one can realise compression factors of 25x in the model obtained by steady learning, and 5x in the model achieved by grokking. Model features and compressibility are then tracked through training. We show that model development in grokking is task-dependent, and that peak compressibility is achieved immediately after the grokking plateau. Finally, novel information-geometric measures are introduced which demonstrate that models undergoing grokking follow a straight path in information space.

  PublisherDOI

• Ising samples 16x16 lattice, 2d, grokking vs learning

  Zenodo (CERN European Organization for Nuclear Research) · 2026-05-01

  datasetOpen access

  Ising dataset associated with Grokking vs. Learning: Same Features, Different Encodings (arXiv:2502.01739).

  PublisherDOI

• Geometry of Contact Terms in Linear Response: Applications to Elasticity

  arXiv (Cornell University) · 2026-03-10

  articleOpen accessSenior author

  Employing the Kubo linear response formalism to calculate the elasticity of anisotropic systems has been shown to yield odd elastic moduli. For Hamiltonian systems, this result seems to be contradictory as it would violate energy conservation. To resolve this discrepancy, we examine the predictions of quantum linear response in the context of our expectation from classical elasticity theory. Our framework reveals that the geometry of the space of strain perturbations introduces correction factors to the correspondence between the Kubo formula and the elastic moduli which resolves the contradiction. We use a two-dimensional gas of electrons in a magnetic field as a pedagogical example. We use generalized f-sum rules to demonstrate how contact terms may reveal themselves in experimental measurements. Finally, we discuss the implications of our results for interpreting more general linear response functions.

  PublisherOA PDF

• Decomposing momentum scales in the Hubbard Model: From Hatsugai-Kohmoto to Aubry-André

  arXiv (Cornell University) · 2026-04-08

  preprintOpen accessSenior author

  The all-to-all momentum coupling of the Hubbard interaction makes interacting lattice models generically unsolvable. In many settings, however, from Peierls instabilities to Moiré superlattice physics, the low-energy behavior is dominated by scattering at a few characteristic wavevectors. We exploit this by constructing a momentum-space clustering scheme that retains only a chosen subset of interaction channels. Our scheme can be considered a generalization of twist-averaged boundary conditions. In proving this, we also prove that our scheme can be considered as a generalization of Hatsugai-Kohmoto (HK) models, and all versions of the HK model previously considered in the literature arise as special cases. This shows that the surprising phenomenological success of HK models arises from their correspondence to the finite-site Hubbard model. In particular, the recently introduced "Momentum-Mixing HK" model corresponds to a specific choice of clustering limit, which is equal to the original finite-site Hubbard model with twist-averaged boundary conditions. Our scheme becomes particularly powerful when a spatially varying potential selects the dominant momentum channels. We demonstrate this on the one-dimensional analogue of interacting moiré systems: the Aubry-André-Hubbard model. We show that for sufficiently strong onsite potential, clusters as small as two sites can recover the ground state energy to below 1% error relative to DMRG benchmarks. This establishes that physically motivated momentum-space truncations can yield accurate low-energy descriptions at feasible computational cost, opening a path toward tractable interacting models of Moiré systems in two dimensions. Code for reproducing all numerical results is available at https://github.com/chainik1125/decomposing-hubbard.

  PublisherDOI

Recent grants

• CAREER: Topology and Geometry in Condensed Matter Systems

  NSF · $533k · 2020–2026

Frequent coauthors

• Maia G. Vergniory

  Donostia International Physics Center

  115 shared

• B. Andrei Bernevig

  Princeton University

  99 shared

• Jennifer Cano

  68 shared

• Zhijun Wang

  47 shared

• Claudia Felser

  34 shared

• Benjamin J. Wieder

  Centre National de la Recherche Scientifique

  33 shared

• Aitzol García‐Etxarri

  Donostia International Physics Center

  26 shared

• Jeremy Blackburn

  24 shared

Education

• Ph.D., Physics

  Yale University

  2015

Awards & honors

• Presidential Early Career Award for Scientists and Engineers…
• Air Force Young Investigator Award (November 2020)
• NSF CAREER Award (June 2020)
• Alfred P. Sloan Foundation Research Fellow (February 2020)
• McMillan Award (August 2019)