Quantum Simulation with Interacting Staggered Fermions

We are investigating different aspects of (1+1) dimensional staggered fermions with quantum computers. The model has a hopping term that connects neighboring sites and a SO(4) invariant four-fermion onsite interaction term. We are studying the time evolution of the theory and the structure of the ground state. The interest in the model stems from the fact that it is thought to be capable of generating a fermion mass without breaking symmetries. It is thought that this feature requires the ground state to have a highly entangled structure. Our model is free from sign problems and can hence be simulated using Monte Carlo methods. This allows us to test our quantum simulations.  We are also investigating the extension of the original model by adding a finite chemical potential to control the number of fermions. This enlarged model has a sign problem and thus can't be easily investigated with the classical simulation. We propose to implement a quantum simulation of this extended model. We are also investigating the model with tensor network renormalization.