Fractons: gauging spin models and tensor gauge theory

Through the PHY 585 reading project course at Stony Brook, I wrote a paper [13] and gave a talk [6] on gauging spin models in an attempt to learn about the burgeoning field of fractons. In particular, the focus was on how gauging the transverse field Ising model can be viewed as Kitaev’s toric code, as well as how gauging sub-system symmetries can lead to gapped fracton models.

This work was extended into a Master’s thesis to include: the interest in fractons and other subsystem codes from quantum information perspective, lattice gauge theory via the Kogut-Susskind formalism, the physical motivation for the toric code by viewing it as QED on the lattice, the tensor gauge theory prescription for gapless fracton models, and fracton field theories. Future work will be aimed at the polynomial shift algebra gauging approach to fracton theories.

The thesis was successfully defended May 13, 2022 [5]. The thesis has since been put on the arXiv [12].

If you are interested in applying to a STEM PhD see my blog post on this site about the application process.

Direct detection of dark matter

Through the 599 Graduate Seminar course at Stony Brook I gave a talk on direct detection of dark matter [7].

The talk covered the evidence we have that dark matter exists, two theorized particles that could be dark matter, and outlined both the traditional particle detection-oriented searches for these particles in addition to new condensed matter discoveries and collaboration that is opening the door to new searches for dark matter.

If you are interested in applying to a STEM PhD see my blog post on this site about the application process.

Twisted bilayer graphene

Through the 598 Graduate Seminar course at Stony Brook I gave a talk on twisted bilayer graphene [8].

The 2004 isolation of graphene led to a Nobel prize ^{1 2} ; the 2018 fabrication of twisted bilayer graphene (TBG) may well lead to another ^{3 4} .TBG has exhibited unconventional superconductivity, a strong-correlated Mott insulator phase, magnetism, topological condensed matter physics, and a strange metal phase. In this talk we will touch on these exotic properties but will also establish some background theory including band theory and the Hubbard Model.

If you are interested in applying to a STEM PhD see my blog post on this site about the application process.

Gravity as a gauge theory

Through the Netherland-America Foundation Fulbright Scholarship, I worked under Professor Eric Bergshoeff, Johannes Lahnsteiner, and Ceyda Şimşek at the University of Groningen reviewing how gravity can be viewed as a gauge theory. After showing how Einstein’s general relativity (GR) can be viewed as a gauge theory of the Poincaré algebra, I reviewed Prof. Bergshoeff’s work showing how Cartan’s geometric formulation of Newtonian gravity (Newton-Cartan gravity) can be viewed as a gauge theory of the Bargmann algebra. In doing so, I reviewed the following auxiliary topics: the extension of Yang-Mills to a more generic formalism of gauge theory, the fiber bundle picture of gauge theory, the vielbein formalism of GR, Lie algebra procedures such as central extensions and İnönü-Wigner contractions, and the hallmarks of Newtonian gravity which differentiate it from GR. Through this work I wrote a pedagogical review paper on the topic that is on the arXiv, and currently has 1 citation [14] and gave a talk to the Van Swinderen Institute’s weekly journal club, which currently has 3000+ views on YouTube [9]. I also wrote a review paper several months before beginning this work on some related topics to prepare for this work [15].

One of the first press releases concerning my receiving the Fulbright Scholarship can be viewed here. If you are interested in applying for the Fulbright see my blog post on this site about the application process.

Holographic superconductors: using AdS/CFT to study unconventional metals

I worked under Professor Sera Cremonini, Erin Blauvelt, Steven Waskie, and Anthony Hoover through the NSF’s REU program at Lehigh University studying quantum field theory (QFT) and the anti-de Sitter/conformal field theory correspondence (AdS/CFT), as well as applying the techniques of holography to understand the dynamics of strongly coupled quantum systems, high temperature superconductors in particular. I worked with Prof. Cremonini to build up a foundation in QFT and holography before beginning my project under Erin. My work was both analytical and numerical, and consisted of identifying the conditions for the onset of a certain class of gravitational instabilities that are related to spatially modulated (striped) instabilities arising in many strongly correlated quantum phases. My work culminated in a research paper that introduced AdS/CFT and the holographic techniques that were involved in our modeling the dynamics of a strongly interacting system [17]. I also had the pleasure of giving a talk to my peers mirroring this paper [11] and gave a slightly simplified version of this talk (with some updated figures) to an audience of math professors and students [10].

If you are interested in applying for an NSF REU summer research experience see my blog post on this site about getting undergraduate research experience.

Optimizing an electron’s path to ionization using a genetic algorithm

I worked under Professor Thomas Carroll with Kevin Choice, Bianca Gualtieri, and Zoe Rowley at my undergraduate institution, Ursinus College, on quantum control simulation that makes use of machine learning genetic algorithms. In particular, we have used supercomputer clusters to simulate the ionization of rubidium atoms in a Rydberg state, and machine-learning genetic algorithms founded on the basis of Darwinian evolution to control that ionization. My work during Ursinus College’s Summer Fellow experience, in addition to my research throughout my junior year, resulted in identifying advantageous parameters to use in our genetic algorithm, establishing some computational limitations of our algorithm through studying target solutions, developing a method of running partial simulations to drastically reduce computation time, discretizing the electric field values used in our simulation to better model our experimental capabilities, as well as redefining the color map of our outputted graphics to allow more seamless rendering and rescalings in image processing software for our research posters and papers.

Through this work I wrote two research papers [16] [18]; presented posters on-campus [19] and at two national conferences, APS DLS 2017 [4] and APS DAMOP 2018 [3]; and co-authored two journal articles, one published in Physical Review A (which currently has 6 citations) [2] and another published in Journal of Physics B (which currently has 1 citation) [1].

Throughout the fall of my senior year, my work focused on improving our ionization model by including the calculation of free state wavefunctions into our Hamiltonian as opposed to only those of bound states. This was done in an effort to increase our knowledge of the electron populations in given energy levels. My work culminated in a research paper (geared at introducing the younger generation of the group to our work) that outlined our new ionization model, introduced object-oriented programming in the context of our model, as well as detailed our development of integration and interpolation techniques to handle the divergent and oscillatory nature of free state wavefunctions [16].

If you are interested in getting research experience in college, please see my blog post on this site about getting undergraduate research experience.

References

Peer-reviewed Publications and Poster Presentations at National Conferences

[1] V. Gregoric et al., Perturbed Field Ionization for Improved State Selectivity, J. Phys. B: At. Mol. Opt. Phys. 53 084003 (2020) [arXiv:1908.09052].

[2] V. Gregoric et al., Improving the state selectivity of field ionization with quantum control, Phys. Rev. A 98, 063404 (2018) [arXiv:1806.00889].

[3] J. Bennett et al., Simulations of directed field ionization, Poster presented at American Physical Society’s (APS) Division of Atomic, Molecular and Optical Physics 2018 meeting. [See poster here].

[4] J. Bennett and K. Choice, Optimizing an electron’s path to ionization using a genetic algorithm, Poster presented at APS Division of Laser Sciences 2017 meeting. [See poster here].

Talks

[5] J. Bennett, Fractons: gauging spin models and tensor gauge theory, Master’s thesis defense, Stony Brook University (2022) [See slides here].

[6] J. Bennett, Lattice gauge theory: toric code and fractons, Reading project talk given to Professor Tzu-Chieh Wei’s research group meeting at Stony Brook University (2021) [See slides here].

[7] J. Bennett, Direct detection of dark matter, Graduate seminar talk given to the 599 course of the physics department at Stony Brook University (2021) [See slides here].

[8] J. Bennett, Twisted bilayer graphene, Graduate seminar talk given to the Physics 598 class at Stony Brook University (2020). [See slides here].

[9] J. Bennett, Gravity as a gauge theory, Department talk given to the Van Swinderen Institute for Particle Physics and Gravity at the University of Groningen (2020). [See slides here].

[10] J. Bennett, Holographic superconductors: using AdS/CFT to study unconventional metals, MATH 350 symposium talk given to the math department at Ursinus College (2018) [See slides here, 2 updated figures from talk below].

[11] J. Bennett, Holographic superconductors: using AdS/CFT to study unconventional metals, Symposium talk given to the physics department and cohort of the 2018 National Science Foundation Research Experience for Undergraduates at Lehigh University (2018). [See slides here].

Review Papers, Research Papers, and Local Poster Presentations

[12] J. Bennett, “Fractons: gauging spin models and tensor gauge theory,” Master’s thesis, Stony Brook University, arXiv:2206.14028 [cond-mat.str-el] (2022).

[13] J. Bennett, Lattice gauge theory: toric code and fractons, Reading project paper written for PHY 585 at Stony Brook University (2021).

[14] J. Bennett, Gravity as a gauge theory, Review paper written at the University of Groningen through the Netherland-America Foundation Fulbright Scholarship, arXiv:2104.02627 [gr-qc] (2020).

[15] J. Bennett, Recent Developments in Non-relativistic Holography, Review paper written through Ursinus College’s senior seminar course (2018).

[16] J. Bennett, Revamped ionization model for Rb atoms in a Rydberg state, Research paper (2018).

[17] J. Bennett, Holographic superconductors: using AdS/CFT to study unconventional metals, Research paper written at Lehigh University through the National Science Foundation Research Experience for Undergraduates program (2018).

[18] J. Bennett and K. Choice, Optimizing an Electron’s Path to Ionization Using a Genetic Algorithm, Research paper written at Ursinus College through the Summer Fellows program (2017).

[19] J. Bennett and K. Choice, Optimizing an electron’s path to ionization using a genetic algorithm, Poster presented at at Ursinus College’s Summer Fellows Symposium (2017).