I am broadly interested in various topics of theoretical physics
Current interests include: critical systems in and out equilibrium, renormalization group flows in generic space of field theories, impurity in static ground states and non-equilibrium dynamics, matrix product states and tensor network states, holography, e.t.c.
Field theories are not all of theoretical physics
Perhaps my research record suggests that I like to working with field theories.
HOWEVER, I do not consider field theories as the answer to everything!
Field theories are useful for extracting universal features, but they are not always the best or only way to describe our real world.
Relying solely on field theories as an effective description of our real world is dangerous! I have always considered lattice models to be a more direct way of accessing the underlying physics of reality. The continuum is a useful tool for understanding complex discrete systems, but it can be too idealized in some cases.
Numerics as experiments for demonstrating theories
Working only on abstract theories makes me feel like I am walking on thin ice. Numerical experiments not only help us verify our theories, but also provide insights and hints about the underlying principles, e.g. by leading to new conjectures. Therefore, I always work in a combination of theory and numerics.
Entanglement as a fundamental concept in many-body physics
In recent years, the study on (long-range) entanglement in many-body systems has brought novel insights to some long-standing problems in many-body physics. I believe there is a chance to find a new paradigm from such crossing, and the study on entanglement in many-body systems could be a trigger of the revolution in modern theoretical physics.
Criticality & Conformal Field Theory
Most of my research focuses on the concept of "Criticality" using the mathematical tool of "Conformal Field Theory." Criticality refers to the properties at the continuous transition point (called the critical point) between different phases of matter. These critical points exhibit identical behaviors that are independent of the microscopic details of the system, a phenomenon known as "Universality." Conformal Field Theory is a mathematical framework used to describe such universality and has wide application ranging from statistical physics to gravitational physics.
A well-known example is the common critical behavior observed between the liquid-gas transition of water and the ferromagnet-paramagnet transition in magnets. This indicates that these two distinct physical systems fall into the same universality class at the critical point. In this specific case, the universality is expected to be described by the Ising Conformal Field Theory, which can be exactly solved in 2d but remains a puzzle in 3d that is directly related to our real life. One amazing thing here is that the phase transition between different phases (ice, liquid, gas) of water seems like a simple question, but it hosts complicated and beautiful physics.
In short, the concept of criticality has a long history in physics, but many aspects of it remain mysteries awaiting exploration. The application and development of conformal field theory would be helpful for advancing research in this direction.