Strongly correlated quantum systems present some of the deepest challenges in modern theoretical physics. Across condensed matter, cold atom physics, lattice field theory, and high-energy theory, one encounters a recurring obstruction: nonperturbative dynamics that evade conventional weak-coupling expansions and, in numerical approaches, sign problems that invalidate Monte Carlo importance sampling. These obstacles limit our ability to explore phase structure, symmetry breaking, and universality in regimes where experimental data are increasingly precise. Two conceptual frontiers motivate my research program:
How to formulate nonperturbative quantum field theories in regimes where standard numerical and perturbative tools fail, such as finite density, strong coupling, or chiral systems on the lattice.
How symmetry breaking, universality, and renormalization group (RG) behavior emerge from first principles, especially when naive semiclassical intuition is unreliable.
My work addresses these questions through a unified strategy combining novel theoretical reformulations, non-Hermitian lattice constructions, and adaptive resummation methods, with concrete applications to ultracold Fermi gases, Gross–Neveu–Yukawa (GNY) models, and scalar field theories. The overarching goal is to build controlled bridges between analytical insight and first-principles numerical simulation.
We work the lattice fermions and non-Hermitian formulation in the 2D GNY model and demonstrate the numerical implementation for two flavors by the Hybrid Monte Carlo. Our approach has a notable advantage in dealing with chiral symmetry on a lattice by avoiding the Nielsen-Ninomiya theorem, due to the non-symmetrized finite-difference operator. We restore the hypercubic symmetry by averaging over all possible orientations with the proper continuum limit. Our study is the first simulation for the interacting fermion formulated in a non-hermitian way. We compare the numerical solution with the one-loop resummation.
The resummation results matches with the numerical solution in $\langle\phi\rangle$, $\langle\phi^2\rangle$, $\langle\mathrm{Tr}(\bar{\psi}_1\psi_1+\bar{\psi}_2\psi_2)/2\rangle$, and $\langle\mathrm{Tr}(\bar{\psi}_1\psi_1+\bar{\psi}_2\psi_2)\phi/2\rangle$. We also used the one-loop resummation to provide the RG flow and asymptotic safety in the 2D GNY model.
From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, the nonrelativistic systems at finite density generally have a sign problem. In the relativistic case, imaginary chemical potentials solve this problem. Is this feasible for nonrelativistic systems? We introduce a complex chemical potential to avoid the sign problem in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.