Speaker
Description
We present results on quantum simulations of topological phases in $(2+1)$D lattice QED with one and two fermion flavors, at both zero and finite density. Establishing that staggered fermions fail to host infrared topological phases, we show that Wilson fermions give rise to Chern-Simons physics in the infrared, reflecting consistency with both the lattice Lagrangian and the continuum formulations. We analyze the topological phase diagram as a function of the fermion masses and couplings for both $N_f=1$, and then $N_f=2$ at finite density which is affected by the sign problem. For the $N_f=2$ theory, we uncover a rich phase diagram, containing regimes that exhibit Integer Quantum Hall and Quantum Spin Hall effects. We analytically prove the robustness of topological observables such as Chern numbers and current correlators despite severe truncation and finite-size effects, making them ideal targets for quantum simulation. Finally, through extensive exact diagonalization calculations for both $N_f=1$ and $N_f=2$, we characterize the spectrum, correlators, and topological invariants, providing a concrete foundation for near-term quantum simulations of topological phases in lattice field theories. We close by outline concrete implementation strategies employed for simulation on superconducting quantum hardware. The talk will be based on https://arxiv.org/pdf/2603.05616 and https://arxiv.org/pdf/2504.21828, and ongoing work.