Prof. Chen-Te Ma

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 discuss the naive lattice fermion without the issue of doublers. A local lattice massless fermion action with chiral symmetry and hermiticity cannot avoid the doubling problem from the Nielsen-Ninomiya theorem. Here we adopt the forward finite-difference deforming the $\gamma_5$-hermiticity but preserving the continuum chiral-symmetry. The lattice momentum is not hermitian without the continuum limit now. We demonstrate that there is no doubling issue from an exact solution. The propagator only has one pole in the first-order accuracy. Therefore, it is hard to know the avoiding due to the non-hermiticity. For the second-order, the lattice propagator has two poles as before. This case also does not suffer from the doubling problem.

Hence separating the forward derivative from the backward one evades the doublers under the field theory limit. Simultaneously, it is equivalent to breaking the hermiticity.

In the end, we discuss the topological charge and also demonstrate the numerical implementation of the Hybrid Monte Carlo.

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.