From tensor networks to quantum computations of lattice field theories
We will explore U(1) lattice gauge theories with topological terms in D=1,2 and 3 spatial dimensions. For D=1, we scrutinize mass perturbation theory at small positive and negative fermion masses, with the latter case being inaccessible for MCMC. In D=2 we provide a resource efficient formulation of the Hamiltonian which can be used for both, tensor networks and quantum computations, and which works for all values of the coupling. In addition, it can be generalized to non-abelian groups and higher dimensions in a straightforward fashion. In our practical example in D=2 we use this formulation to simulate negative fermions masses and find an indication of a phase transition. In D=3 we provide a Hamiltonian formulation of the topological term, including non-abelian theories and explore the phase diagram of the model. Our results suggest a second order topological phase transition at strong coupling.
Live streaming: QuantHEP Seminar YouTube channel