is one of the first Postdocs to be awarded the MCQST Distinguished PostDoc Fellowship. She joined MCQST and the group of Simone Warzel at the Mathematics Departement at TU Munich in 2019 and is an active member of the MCQST community. We invited Amanda to share some insight into her projects, motivation for quantum research, and interests outside her work.
Can you briefly explain your research project?
My research focuses on questions related to the classification of quantum phases of matter. Models in the same phase have similar physical properties, and so having a good understanding of these phases is vital to mapping the physical landscape. For motivation, one can first think of classical phases of matter, which include solids, liquids, and gases. A key ingredient for studying phases is the temperature. Higher temperatures correspond to more energy which can change the phase of the system, such as when a liquid transitions to a gas. Even within a single phase, being able to further refine the classification using other physical characteristics can be helpful to understanding how systems behave. For example, the thickness (or viscosity) of a liquid plays an important role in fluid dynamics.
For quantum many-particle systems, there is still much to explore in the classification of quantum phases of many particle systems. I deal specifically with systems at low temperature, for which the system should be in a low energy state. An important class of phases to investigate in this setting are gapped ground state phases, where the lowest possible energy (called the ground state energy) is separated from all possible higher energies by a nonzero gap. This energy gap indicates that the ground state is protected, meaning if a system is in the lowest energy state, then you can only change the physically observed properties of the system by adding enough energy to overcome the gap. If less energy is added, the system will stay in the ground state. This gap protection is particularly useful for developing quantum devices, where you often need to prevent the state of the system from changing in the presence of the heat created from running the device. For an analogy, one can think of a computer, where you don’t want the heat created from using the computer to cause errors in the memory.
While gapped ground state phases are of particular interest, it is notoriously difficult to show that a many-body model has an energy gap. Moreover, proofs of many physical characteristics (such as exponential clustering, area laws, adiabatic theorems, etc.) often begin with the assumption that the physical model is in a gapped ground state phase, giving even more importance to studying this regime. One aspect of my research focuses on proving energy gaps for key many-body quantum systems. Recently, we were successful at proving a gap on a truncated version for the ⅓-filled Haldane pseudopotential for the fractional quantum Hall effect. While numerical evidence supports the long standing conjecture that this model is gapped, ours is the first analytically rigorous result to support this claim. We are currently investigating how to prove similar results for other fillings as well as exploring how to tackle the untruncated model.
A second pillar of my research focuses on the stability of spectral gaps. Once a gapped is proved, a natural question is whether that model is a good representative of a gapped ground state phase. One way to positively answer this question is to determine if the gap persists in the presence of small perturbations to the system. Bravyi, Hastings and Michalakis introduced a method for proving stability for quantum spin models with topologically ordered ground states. In several works with collaborators, I have investigated how to extend this result in a variety of new directions, including more general graphs and boundary conditions, models with discrete symmetry breaking, models with low-lying edge states, and lattice fermion systems.
"My favorite part of my job is that I get to keep learning, and solve puzzles. It’s really fulfilling when you discover some new insight that provides new understanding for the question at hand and ultimately leads you to the solution."
What does your day-to-day work look like?
My days can vary a bit depending on the tasks I need to complete. I always start my day by checking the new research articles posted to arXiv. Afterwards, the day will consist of some combination of reading papers, working on research projects, talking with collaborators, participating in seminars and group meetings.
What keeps you excited and makes you want to start work in the morning?
My favorite part of my job is that I get to keep learning, and solve puzzles. It’s really fulfilling when you discover some new insight that provides new understanding for the question at hand and ultimately leads you to the solution.
What inspired you to become a quantum scientist? Did you always know you wanted to be a scientist?
I didn’t really “know” what I wanted to do when I was younger, but I always loved my math and science classes. Moreover, my math courses were my favorite during my first year of undergraduate studies, which motivated me to declare applied math as my major.
Coming from a math background, I really enjoy the diversity of mathematics used for studying mathematical physics. The fact that I went into quantum research was a result of doing an undergraduate research experience with the professor who would later become my PhD advisor. I really enjoyed the problems I worked on during that time and decided to continue in that direction.
What drew you to Munich?
As a PhD student, many of the junior and senior researchers that I met had spent at least part of their academic career in Munich. Hearing about their experiences, I really liked that there were multiple institutions with strong mathematical physics programs that engaged with one another. Munich is a powerhouse in math physics research, so it was a no-brainer for me to want to come here.
"Start thinking early on where you want to take your career, and how you can best serve that goal now. Your goal may change as time goes on, but the effort is never wasted."
What are the biggest challenges that you’ve faced, and how have you overcome them?
One specific challenge that comes to mind is balancing teaching and research responsibilities. In my last position, I was in charge of a full load of courses during the academic term, which came with more firm deadlines and requirements. It is very easy to prioritize teaching duties over research projects, which don’t necessarily have a fixed timeline. Finding ways to protect my research time was key. For me, I found that I do research more effectively in the afternoon, so I would take care of my teaching responsibilities in the morning to free up my afternoons for research tasks.
What was your most memorable moment or proudest achievement?
Finishing and submitting my PhD dissertation. It was a physical representation of what I had learned and accomplished over the course of the program. My university did not have a final defense, so it was also the final milestone in my graduate student experience.
Outside of science, what do you enjoy doing most?
I like giving myself projects and trying/making new things, such as baking new desserts, planting gardens, sewing, etc. During quarantine, I took time to learn how to knit. I also enjoy being outside and going to new places. I can’t wait for travel to open up again so I can explore Germany and Europe more.
If you weren't a scientist, what do you think you would be doing now?
After completing my Bachelor’s degree, I worked for two years as a private instructor for homeschooled children. I enjoyed being my own boss, so I think I’d likely be a small business owner.
What advice would you give to someone at the beginning of their science career?
Start thinking early on where you want to take your career, and how you can best serve that goal now. Your goal may change as time goes on, but the effort is never wasted. Also, engage with your community and talk with senior researchers. Being integrated into the research community is particularly beneficial when transitioning into a new phase in your career.