symmetry routes to quantum matters
My research interests lie broadly in the physics of strongly interacting quantum many-body systems in and out of equilibrium with an emphasis on the effects due to the presence of global symmetries. I am also very interested in topics at the intersection of condensed matter, quantum field theory and quantum information.
*Under construction*
Progress in condensed matter and quantum information has equipped us with efficient tools to understand, engineer and manipulate systems with numerous interacting objects. While the rules that govern their dynamics are simply those of quantum and classical mechanics, the task of applying it to complicated systems is often daunting. However, certain principles have greatly aided us in making progress - locality, universality and symmetry. Not only do these principles help us give a sharp theoretical definition of a phase of matter as an equivalence class systems governed by local Hamiltonians, but they allow us to study properties of physically realistic but complicated systems belonging to a phase by using simple toy models which we can reliably study. Additionally, they guide us in finding suitable tools to characterize and probe physical systems like order parameters and linear responses. In this spirit, the questions I am currently interested in are:
When is the ergodic hypothesis applicable? When ergodicity is broken, is there always a modified variant of statistical mechanics that can be used?
What is the precise relationship between equilibrium phases of matter and the universality class of transitions between them?
Can we classify gapless phases as successfully as we did gapped ones?
How do measurements affect strongly correlated many-body states? Can we control the outcome sufficiently to perform measurement based quantum computation?
How do symmetries emerge? How can we use emergent symmeties and structures to understand condensed matter phenomena better?
Below, I will briefly describe projects I am working on or have worked on in attempting to answer these questions.