Katherine Van Kirk

MASt Applied Mathematics ("Part III"), Cambridge University (2020)
B.S.H Engineering Physics, Stanford University (2019)

Katherine worked with the Houck group through the QURIP program (joint quantum research program between Princeton and IBM). Her work in the lab included (1) simulating magnetic lattices, (2) exploring different theoretical approaches to calculating hopping rates, and (3) investigating interesting properties/patterns in lattice band structures,

Recent Publications

L. Stefanazzi, et al., “The QICK (Quantum Instrumentation Control Kit): Readout and control for qubits and detectors,” Review of Scientific Instruments, 2022. Publisher's Version

C. S. Chiu, A. N. Carroll, N. Regnault, and A. A. Houck, “Line-graph-lattice crystal structures of stoichiometric materials,” Physical Review Research, vol. 4, pp. 023063, 2022. Publisher's Version Abstract

The origin of many quantum-material phenomena is intimately related to the presence of flat electronic bands. In quantum simulation, such bands have been realized through line-graph lattices, a class of lattices known to exhibit flat bands. Based on that work, we conduct a high-throughput screening for line-graph lattices among the crystalline structures of the Materials Flatband Database and report on new candidates for line-graph materials and lattice models. In particular, we find materials with line-graph-lattice structures beyond the two most commonly known examples, the kagomé and pyrochlore lattices. We also identify materials which may exhibit flat topological bands. Finally, we examine the various line-graph lattices detected and highlight those with gapped flat bands and those most frequently represented among this set of materials. With the identification of real stoichiometric materials and theoretical lattice geometries, the results of this work may inform future studies of flat-band many-body physics in both condensed matter experiment and theory.

A. Petrescu, et al., “Accurate methods for the analysis of strong-drive effects in parametric gates,” arXiv, 2021.

D. - S. Ma, et al., “Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices,” Physical Review Letters, vol. 125, pp. 266403, 2020. Publisher's Version

C. S. Chiu, D. - S. Ma, Z. - D. Song, B. A. Bernevig, and A. A. Houck, “Fragile topology in line-graph lattices with two, three, or four gapped flat bands,” Physical Review Research, vol. 2, pp. 043414, 2020. Publisher's Version Abstract

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: Their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.

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Houck Lab

Quantum computing and condensed matter physics with microwave photons

Katherine Van Kirk

Katherine Van Kirk

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Recent Publications