My research lies at the interface of quantum field theory and lattice field theory. A central goal of my work is to develop analytical and numerical tools for nonperturbative quantum systems, particularly in regimes where conventional methods fail, such as those with strong coupling and sign problems. A unifying theme across my research is the exploration of non-Hermitian formulations, lattice constructions, and analytic continuation techniques as new frameworks for overcoming longstanding obstacles in quantum field theory. These include the fermion doubling problem, the sign problem in Monte Carlo simulations, and the limitations of conventional perturbation theory. My contributions can be grouped into two main directions:
Non-Hermitian lattice field theory and fermion formulations
Numerical and analytical methods for strongly interacting fermionic systems
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.